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Sheldon  &   Company's    Text-Books. 
PROFESSOR    OLNEY'S 

NEW   MATHEMATICAL    SERIES 


The  success  of  Prof.  Oluey's  series  lias  been  most  wonderful. 

With  all  their  admitted  excellencies,  both  the  Author  and  Pub- 
lishers have  felt  that  it  was  possible  to  retain  their  many  attractive 
features  and  yet  adapt  the  books  more  perfectly  to  the  special 
school-room  wants. 

To  accomplish  this  most  desirable  end,  Professor  Olney  has  been 
accumulating  very  valuable  suggestions.  He  has  also,  for  several 
years,  had  associated  with  him  in  the  preparation  of  this  new 
series,  some  of  the  best  practical  teachers  in  the  country. 

The  design  is  to  present  to  the  educational  public  the  best  and 
most  teachable  series  of  Mathematics  ever  published.  The  work 
is  now  so  far  advanced  that  the  Publishers  are  able  to  make  the 
above  pleasing  announcement,  which  they  feel  will  be  of  great 
interest  to  all  who  are  engaged  in  teaching. 


THE    NEW  SERIES    EMBRACES: 

i. 
Olney's  First  Lessons  in  Arithmetic.    JUST  PUBLISHED. 

n. 
Oluey's  Practical  Arithmetic. 

This  book  has  been  published  but  a  short  time,  but  it  has 
already  had  the  most  wonderful  success. 
They  are  models  of  beauty  and  cheapness. 


For  schools  of  a  high  grade,  Professor  Olney  has  prepared — 
I  in. 

The  Science  of  Arithmetic. 

IT. 

The  First  Principles  of  Algebra. 

AN  INTRODUCTION  TO  THE   AUTHOR'S  COMPLETE  AND 
UNIVERSITY  ALGEBRAS. 

Y. 

Olney's  Complete  Algebra.   NEW  EDITION,  IN  LARGE  TYPE. 
This  book  is  now  entirely  re-el  ectrotyped  in  larger  and  more 
attractive  type.    The  explanatory  matter'is  greatly  lessened.    The 
attractive  features  of  this  book,  which  have  made  it  the  most 
popular  Algebra  ever  published  in  this  country,  are  all  retained. 


~>  f*'\heldon  <&  Company's  Text-Sooti*        *• 

X*/  ^rrV 

rie  ^kience   o/    Government   in    Connect  $  ^ 
Amqfacan  Institutions.    By  JOSEPH  ALDEN,  Dip., 
Pre|Vdj  State  Nonnal  School,  Albany.    1  voL  12mo. 
the  wants  of  High  Schools  and  Colleges. 


Manual:  a  Text-Book  on  Government,  in 
American  Institutions,  adapted  to  the  wants  of 
Common  Schools.  It  is  in  the  form  of  questions  and  answers. 
By  JOSEPH  ALDEN,  D.D.,  LL.DH  1  vol.  16mo. 

Hereafter  no  American  can  be  said  to  m-^ducated  who  does  not  thoroughly 
understand  the  formation  of  our  Go/'ermrfct.  A  prominent  divine  has  said, 
that  "  every  young  person  should  car^f^ily  pidkonscieutiously  be  taught  those 
distinctive  ideas  which  constitute  tlur£ijb?taiic<»  our  Constitution,  and  which 
determine  the  policy  of  our  politics^  aad  to  tbj^  <jnd  there  ought  forthwith  to 
be  introduced  into  our  schools  a  simple,  comgfrekensive  manual,  whereby  the 
needed  tuition  should  be  implanted  at  that  early  period. 

Long's  Classical  Atlas.  Constructed  by  WILLIAM  HUGHES, 
and  edited  by  GEORGE  Loi»,  formerly  Professor  of  Ancient 
Languages  in  the  Universiw  of  Virginia.  With  a  Sketch  of 
Ancient  Geography,  and  other  ^ffftditions,  by  the  American 
Editor.  Containing  Fifty -two  Colored  Maps  and  Plans  on 
Twenty-two  large  imperial  quarto  Plates,  beautifully  engraved 
on  steel.  With  an  index  of  Places. 

Royet's  Thesaurus  of  English  Words  and  Phrases, 

so  classified  Ad  arranged  as  to  facilitate  the   expression   of 
ideas,  and- assia>  m  literary  composition.     By  PETER  MARK 
ROGET.     B,evisea*?had  edited,  with  a  List  of  Foreign  Words 
denned  in  HnglMiTttkd  other  additions,  by  BARNAS  SEARS,  D.D.,   j 
late  President  orVBrown  University.     A  new  American,  from   ! 
the  last  London  dlitioii,  with  important  Additions,  Corrections, 
and  Improvement*     12mo,  cloth. 

Fairchilds*  Moral  Philosophy;  or,  The  Science  of 
Obligation.  BY  J.  H.  FAIRCHILDS,  President  of  Oberlin 
College.  1  vol.  12mo. 

The  aim  of  this  volume  is  to  set  forth,  more  fully  than  has  hitherto  been 
done,  the  doctrine  that  virtue,  in  its  elementary  form,  consists  in  benevo- 
lence, and  that  all  forms  of  virtuous  action  are  modifications  of  this  principle. 

After  presenting  this  view  of  obligation,  the  author  takes  up  the  questions  of 
Practical  Ethics,  Government  and  Personal  Rights  and  Duties,  and  treats 
them  in  their  relation  to  Benevolence,  aiming  at  a  solution  of  the  problems  of 
right  and  wrong  upon  this  simple  principle. 


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1ST  B  -W     REVISED     E  r>  I  T  I  O  JST. 


THE 


INTELLECTUAL  AEITHMETIC  : 


CONTAINING 


AN  EXTENSIVE  COLLECTION  OF  PRACTICAL  QUESTIONS 
ON  THE  GENERAL  PRINCIPLES  OF  ARITHMETIC. 


Concise  nub  (®riwal     lciljobs  of 


WHICH    SIMPLIFY  MANY   OF   THE    MOST  IMPORTANT  RULES 
WRITTEN  ARITHMETIC. 


BY 

JOHN"  F.  STODDARD,  A.M., 

AUTHOR  OP   THE    "NORMAL  MATHEMATICAL   SERIES,"   ET<X 


NEW     YORK: 

SHELDON  &  COMPANY, 

No.   8    MURRAY    STR.EET. 


STODDARD'S  SERIES  OF  ARITHMETICS. 


STODDARD'S  JUVENILE  MENTAL  ARITHMETIC. 
"  INTELLECTUAL  " 

"  RUDIMENTS  OF  " 

«*  NEW  PRACTICAL  " 


SHORT     COURSE. 

STODDARD'S- PRIMARY  PICTORIAL  ARITHMETIC 
"  COMBINATION  SCHOOL         " 

"  COMPLETE  " 


OLNEY'S  HIGHER  MATHEMATICS. 

OLNEY'S  INTRODUCTION  TO  ALGEBRA 

"        COMPLETE  SCHOOL        "         

"       UNIVERSITY  "        

"        TEST  EXAMPLES  IN       " 

"        GEOMETRY 

"       TRIGONOMETRY 

"       GEOMETRY  AND  TRIGONOMETRY,  School  Edition. 

University  Ed 
"     CALCULUS.. 


Entered,  according  to  Act  of  Congress,  in  the  year  1849,  by 

JOHN    F.    STODDARD, 

In  tha  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the  Southern, 
District  of  New  York. 

Re-entered,  according  to  Act  of  Congress,  in  the  year  1866,  by 

SHELDON    &    COMPANY, 

t-  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the  Southern 
District  of  New  York. 


PREFACE. 


HAVING  felt  the  necessity  of  a  more  extended  and  systematic 
Intellectual  Arithmetic  for  younger,  as  well  as  more  advanced 
pupils,  I  prepared  and  used  in  manuscript,  in  my  own  school, 
for  a  number  of  years,  such  a  series  of  questions  as  I  deemed 
best  adapted  to  the  purpose.  After  observing  the  superior 
mental  training  derived  from  their  use,  and  the  ease  with 
which  pupils  thus  trained  comprehended  the  more  advanced 
branches  of  mathematics,  I  venture  to  submit  them  to  the 
public  in  the  following  pages,  hoping  that  they  may  prove  as 
useful  to  other  schools  as  they  have  to  my  own. 

The  rule  which  I  have  observed  in  preparing  this  work  is: 
Tell  but  one  thing  at  a  time,  and  that  in  its  proper  place. 

Although  in  many  particulars  the  work  differs  from  other 
"Mental"  Arithmetics,  as  an  examination  of  the  "questions" 
will  show,  mention  of  these  differences  is  omitted,  and  the  fot-^ 
lowing  exposition  of  its  arrangements  of  subjects  is  presented.  * 

Chapters  First,  Second,  Third,  and  Fourth,  from  Lesson  I  to 
Lesson  XV,  treat  respectively  of  Addition,  Subtraction,  Mul- 
tiplication, and  Division  of  simple  numbers  ;  each  of  which 
is  rendered  familiar  by  an  extensive  collection  of  practical 
questions.  Lesson  VII  consists  of  questions  which  combine 
Addition  and  Subtraction  ;  Lesson  IX,  of  questions  combining 
Addition,  Sabtraction,  and  Multiplication  ;  Lesson  XIII,  of 
questions  combining  the  twelve  previous  Lessons  ;  and  Lesson 
XIV,  of  questions  in  Proportion.  Thus,  an  intimate  connec- 
tion between  Lessons  and  even  Chapters  is  kept  up  through 
the  entire  work,  with  the  exception  of  Chapter  Fifth,  Lesson 
XIV  to  Lesson  XXVII,  which  contains  some  of  the  most  im- 
portant Tables  of  Weights  and  Measures  ;  each  of  which  is 
illustrated  with  appropriate  questions. 

Chapter  Sixth,  from  Lesson  XXVI  to  Lesson  XL  VI,  is  de- 
voted to  the  subject  of  Fractions,  in  which  twenty  lessons  are 
many  original  combinations  of  numbers  and  concise  analyses. 

Chapter  Seventh,  from  Lesson  XL  VI  to  Lesson  LIX,  consists 
of  practical  and  intricate  questions  of  various  kinds,  which 
require  for  their  solution  a  thorough  knowledge  of  the  preced* 


IV  P  K  E  F  A  G  E  . 

ing  Chapters.  This  Chapter  (perhaps  not  contained  in  any 
similar  work),  when  understood,  will  be  of  great  benefit  to 
those  who  are  studying,  or  who  intend  to  study  Algebra. 

Chapter  Eighth,  from  Lesson  LIX  to  the  end,  includes  Inter- 
est, Discount,  and  Per  Cent.,  in  their  various  modifications. 
The  method  of  treating  these  subjects  is  original ;  and  renders 
the  rules  under  these" heads,  in  Written  Arithmetics  (which 
are  often  incomprehensible  to  pupils),  perfectly  intelligible,  by 
reducing  the  whole  to  one  continued  train  of  reasoning. 

This  Chapter,  thoroughly  taught,  can  not  fail  to  quicken, 
strengthen,  and  develop  the  reasoning  powers.  Bringing  into 
exercise,  as  thorough  teaching  of  it  will,  nearly  eveiy  principle 
taught  in  the  twenty  lessons  of  Chapter  Sixth,  and  also  the 
greater  part  of  Chapter  Seventh,  the  pupil  will  acquire  the 
habit  of  systematically  classifying  his  knowledge,  and  be  en- 
abled to  call  to  his  aid  such  portions  of  it  as  will  assist  in 
illustrating  or  demonstrating  the  subject  under  consideration. 

That  Intellectual  Arithmetic,  when  properly  taught,  is  better 
calculated,  than  any  other  study,  to  invigorate  and  develop  the 
reasoning  faculties  of  the  mind,  to  produce  accurate  and  close 
discrimination,  and  to  enable  the  pupil  to  acquire  a  knowledge 
of  the  Higher  Mathematics  with  greater  ease,  can  scarcely 
admit  of  a  doubt. 

J.  F.  STODDARD. 

NEW  YOKE,  August  1, 1860. 


PUBLISHERS'  NOTE. — A  new  edition  of  this  popular  Intel- 
lectual Arithmetic,  carefully  revised  by  the  author,  is  here 
presented  in  new  and  larger  type,  and  on  larger  pages,  without 
any  changes  which  might  interfere  with  its  use  in  the  same 
classes  with  previous  editions.  The  "  Lessons"  are  numbered, 
in  regular  order,  throughout  the  book.  In  Lesson  XXVI  are 
full  Tables  of  Metrical  Weights  and  Measures  on  the  Decimal 
System,  the  simplicity  of  which  is  an  important  consideration 
for  instructors  of  youth. 

Prof.  Stoddard's  new  Key  to  this  book,  containing  his  Methods 
of  Teaching  Intellectual  Arithmetic,  is  now  published 


SUGGESTIONS   TO   TEACHERS. 


FOB  the  benefit  of  those  whose  experience  in  teaching  Men- 
tal Arithmetic  is  limited,  the  following  suggestions  are  made 
of  such  methods  of  teaching  this  important  subject,  as  may 
prove  best  suited  to  fix  the  attention,  strengthen  the  memory, 
develop  the  reasoning  powers,  and  secure  rapid  and  accurate 
computation. 

One  thing  at  a  time  should  be  taught,  thoroughly,  and  in  its 
proper  order. 

Recitations  and  exercises  for  children  should  be  short,  and 
during  their  continuance  the  careful  attention  of  each  member 
of  the  class  should  be  secured,  and  thereby  animation  and 
promptness  will  be  encouraged. 

The  lesson  should  be  assigned  previous  to  recitation,  to 
afford  the  pupils  an  opportunity  for  an  examination  and  study 
of  it ;  and  during  class  exercise,  pupils  should  not  use  the 
book. 

Drills,  Illustrations,  and  Explanations  should  occupy  at  least 
one  half  of  the  time  devoted  to  each  recitation  for  children. 

Care  should  be  taken  that  the  positions  of  children  should 
be  good,  and  that  the  language  used  be  strictly  correct  in 
articulation,  pronunciation,  and  construction,  and  addressed  to 
the  person  asking  the  question.  Both  listlessness  and  hurried 
solutions  should  be  avoided ;  in  the  latter,  pupils  not  unfre- 
quently  pronounce  and,  if,  what,  costs,  quarts,  as  follows,  an,  ef, 
wat,  eoss,  quats.  By  careful  attention  to  these  particulars, 
lessons  in  Intellectual  Arithmetic  will  be  valuable  exercises  in 
address,  elocution,  grammar,  rhetoric,  and  logic,  and  pupils 
will  acquire  both  a  ready  command  of  their  thoughts,  and  a 
fluency  of  language  in  expressing  them. 

A  Question  should  be  read  slowly  and  distinctly,  and  a 
pupil  be  required  to  repeat  it  accurately,  and  analyze  it  thor- 
oughly, according  to  the  forms  given.  There  should  be  no 
interruption,  except  when  the  teacher  deems  it  necessary  to 
make  a  correction  or  an  important  criticism. 


VI  SUGGESTIONS     TO     TEACHERS. 

Pupils  should  be  called  upon  promiscuously,  and  not  in 
rotation,  to  take  part  in  the  recitation. 

Class  Drills  should  not  be  employed  as  a  regular  method  of 
recitation,  but  simply  to  fix  in  the  minds  of  pupils  such  tab- 
ular facts  as  can  more  readily  be  learned  by  concert  recitation, 
to  enliven  the  exercises,  to  give  animation  to  the  class,  and 
confidence  to  the  timid  pupils. 

Combinations  of  figures  in  the  Tables  should  be  thoroughly 
learned  by  the  pupil,  and  both  rapidity  and  accuracy  should 
characterize  his  operations  in  Addition  before  he  is  required 
to  study  other  parts  of  the  subject.  As  aids  to  this  result, 
exercises  such  as  the  following  may  be  made :  the  teacher  may 
give  out  the  number  6,  and  require  each  member  of  the  class 
to  write  on  his  slate  the  various  combinations  of  two  numbers, 
with  the  proper  signs,  that  will  produce  the  given  number. 
Most  pupils  will  at  first  perform  this  exercise  in  an  irregular 
manner,  and  the  teacher  should  instruct  them,  by  forming  the 
proper  arrangement  on  the  blackboard  and  explaining  it. 

PUPIL'S  ARRANGEMENT.  TEACHER'S  ARRANGEMENT. 


2+4  =  6 

1  +  5  =  6 

4  +  2=6 

5  +  1=6 
3  +  3=6 


5+1=6  6=1+5 

4+3=6  6=2+4 

3  +  3=6  or,  6  =  3  +  3 

2+4=6  6=4+2 

1+5=6  6=5+1 


Similar  exercises  may  be  had  on  Subtraction,  Multiplication, 
and  Division,  with  the  appropriate  signs. 

Every  combination  of  this  arrangement  may  be  illustrated 
•with  objects,  such  as  pebbles,  grains  of  corn,  beans,  so  that  the 
class  may  clearly  understand  each. 

A  pupil  thoroughly  drilled  in -the  fundamental  operations 
of  Arithmetic,  will  not  only  be  able  to  perform  them  with 
facility  and  accuracy,  but  will  have  made  great  progress 
toward  an  easy  and  complete  mastery  of  the  Science  of  Num- 
bers. 

The  advantages  of  this  exercise  are,  that  it  insures  a  thorough 
knowledge  of  the  Tables;  it  teaches  to  write  figures  and  signs 
properly;  it  gives  pleasant  employment  to  the  bodies  and 
minds  of  pupils,  and  therefore  helps  to  secure  good  order. 

More  explanations  on  Methods  of  Teaching  Intellectual 
Arithmetic,  are  presented  in  the  new  Key  to  this  work,  which 
book  may  be  a  valuable  assistant  to  those  who  have  found 
difficulties  in  using  Stoddard's  Intellectual  Arithmetic. 


ARITHMETIC. 


ADDITION. 

Addition  is  the  process  of  uniting  like  numbers 
into  one  sum. 

The  Sum,  or  Amount,  is  a  number  equal  to  all 
the  numbers  added. 


LESSON     I. 

1.  2     and     1     are     how 
ANALYSIS. — Two  and  one  are  three. 

2.  2     and     2     are    how 
2     and     3     are     how 
2     and    4    are     how 
2     and     5     are    how 
2     and     6     are    how 
2     and     7    are    how 
2     and     8     are     how 
2     and     9     are     how 

and     2     are     how 


3- 

4- 

6.' 


9- 

10. 

ii. 

12. 

'3- 

14. 
15. 
16. 
17. 
18. 
'9- 

20. 
21. 
22. 

23. 
24. 


3  and  3  are  how 

3  and  4  are  how 

3  and  5  are  how 

3  and  6  are  how 

3  and  7  are  how 

3  and  8  are  how 

3  and  9  are  how 

4  and  3  are  how 
4  and  4  are  how 
4  and  5  are  how 
4  and  6  are  how 
4  and  7  are  how 
4  and  8  are  how 
4  and  9  are  how 


many? 

many  ? 
many  ? 
many  ? 
many  ? 
many? 
many  ? 
many? 
many? 
many? 
many  ? 
many? 
many? 
many? 
many? 
many? 
many  ? 
many  ? 
many? 
many  ? 
many? 
many  ? 
many  ? 
many  ? 


8  ADDITION. 

25.  James  killed  2  birds,  and  John  killed  1  bird ;  how 
many  birds  did  both  kill  ? 

ANALYSIS. — If  James  killed  2  birds  and  Jokn  1,  they 
together  killed  2  birds  and  1  bird,  which  are  3  birds. 

26.  I  gave  2  cents  to  Henry,  and  2  cents  to  Harvey ; 
how  many  cents  did  both  receive  ? 

27.  Hiram  had  2  cents,  and  his  brother  gave  him  3 
cents  more ;  how  many  cents  had  he  then  ? 

28.  George  gave  me  2  apples,  and  Mary  gave  me  4 
apples ;  how  many  apples  did  both  give  me  ? 

29.  A  man  had  2  cows,  and  he  purchased  5  cows 
more ;  how  many  cows  had  he  then  ? 

30.  John's  father  gave  him  2  oranges,  and  his  mother 
gave  him  6 ;  how  many  did  he  receive  ? 

31.  Philo  bought   2  peaches,  and  his  brother  gave 
him  7 ;  how  many  peaches  had  he  then  ? 

32.  Philip  gave  me  2  plums,  and  Myron  gave  me  8  ; 
how  many  plums  did  they  together  give  me  ? 

33.  A  farmer  had  2  horses,  and  bought  9  more ;  how 
many  horses  had  he  then  ? 

•34.  William  had  3  oranges,  and  Moses  gave  him  2 
more ;  how  many  had  he  then  ? 

35.  John  bought  3  apples,  and  I  gave  him  3 ;  how 
many  had  he  then  ? 

36.  Philip  paid  3  cents  for  some  nuts,  and  4  cents  for 
some  candy ;  how  many  cents  did  he  pay  for  both  ? 

37.  I  paid  5  cents  for  some  paper,  and  3  cents  for  a 
stamp ;  how  much  did  I  pay  for  both  ? 

38.  A  merchant  bought  3  barrels  of  sugar  and  6  bar- 
rels of  molasses ;  how  many  barrels  did  he  buy  ? 

39.  Ealph  is  3  years  old,  and  Edward  is  7 ;  what  is 
the  sum  of  their  ages.? 

40.  A  lemon  cost  3  cents,  and  a  pine-apple  cost  8 ; 
what  sum  did  both  cost  ? 

41.  James    solved   3   questions   in    arithmetic,   and 
Oliver  9 ;  how  many  did  both  solve  ? 


ADDITION.  9 

42.  If  it  take  4  yards  of  cloth  for  a  c/>at,  and  1  yard 
of  cloth  for  a  vest,  how  many  yards  will  it  take 
for  both  ? 

43.  Samuel   bought  4  marbles,  and  found  4 ;   how 
many  marbles  had  he  then  ? 

44.  Isaac  bought  4  sheets  of  paper,  and  I  gave  him  5  ; 
how  many  had  he  then '( 

45.  A  man  bought  an  apple  for  4  cents,  and  a  pear 
for  6  cents ;   how  much  did  the  apple  and  pear 
together  cost '( 

46.  If  Mary  has  4  books,  and  her  father  should  give 
her  7,  how  many  books  would  she  then  have  't 

47.  William  has  4  marbles  in  his  hand,  and  8  in  his 
pocket ;  how  many  marbles  has  he  in  all  ? 

48.  Charles  walked  4  miles,  and  rode  9 ;  how  many 
miles  did  he  go  ? 

49.  In  a  certain  class  there  are  5  boys,  and  4  girls; 
how  many  pupils  are  in  the  class  ? 


LESSON     II. 

1 .  5  and  4  are  how  many  ? 

2.  5  and  5  are  how  many  ? 

3.  5  and  6  are  how  many  ? 

4.  5  and  7  are  how  many  ? 

5.  5  and  8  are  how  many  ? 

6.  5  and  9  are  how  many  ? 

7.  6  and  5  are  how  many  ? 

8.  6  and  6  are  how  many  ? 

9.  6  and  7  are  how  many  ? 
10.  6  and  8  are  how  many? 
u.  6  and  9  are  how  man}7? 

12.  7  and  6  are  how  many? 

13.  7  '  and  7  are  how  many? 

14.  7  and  8  are  how  many  ? 

15.  7  and  9  are  how  many? 


10  ADDITION. 


1  6. 

,8 

and 

7 

are 

how 

many  ? 

17. 

8 

and 

8 

are 

how 

many  ? 

18. 

8 

and 

9 

are 

how 

many  ? 

19. 

8 

and 

5 

are 

how 

many  ? 

20. 

9 

and 

6 

are 

how 

many? 

21. 

9 

and 

8 

are 

how 

many  ? 

22. 

9 

and 

9 

are 

how 

many  ? 

23. 

9 

and 

10 

are 

how 

many  ? 

24. 

9 

and 

7 

are 

how 

many  ? 

25. 

9 

and 

T          K 

11 

are 

how 

many  ? 

26.  Mary  answered  5  questions  correctly,  and  4  in- 
correctly ;  how  many  questions  did  she  answer  ? 

27.  A  beggar  met  two  boys ;   one  gave  him  5  cents, 
and  the  other  gave  him  6  cents ;  how  many  cents 
did  both  give  him  ? 

28.  A  man  bought  a  hat  for  5  dollars,  and  a  pair  of 
boots  for  6  dollars ;  how  much  did  he  pay  ? 

29.  There  are  9  boys  on  one  bench,  and  8  on  an- 
other ;  how  many  are  on  both  ? 

30.  Maria  gave  her  teacher  5  pinks  and  7  roses ;  how 
many  nowers  did  she  give  him  ? 

31.  Harry  caught  5  squirrels,  and  Henry  caught  8; 
how  many  were  caught  by  both  ? 

32.  If  we  learn  5  pages  this  week,  and  9  next,  how 
many  shall  we  learn  in  the  two  weeks? 

33.  Frank  sold  a  melon  for  6  cents,  and  an  orange 
for  5  cents ;  for  how  many  cents  did  he  sell  both  ? 

34.  John  bought  6  whips,  and  Joseph  gave  him  6 ; 
how  many  had  John  then  ? 

35.  George  had  6  chestnuts,  and  Richard  gave  him  7; 
how  many  had  George  then  ? 

36.  Henry  bought  6  figs,  and  Sarah  bought  8 ;  how 
many  were  bought  by  both  ? 

37.  Rebecca  has  6  oranges,  and   Catherine  has  9 ; 
how  many  oranges  have  both  ? 

38.  A  boy  bought  7  apples,  and  his  father  gave  him 
6  ;  how  many  liad  he. then  ? 


ADDITION.  11 

39.  Minerva  bought  7  yards  of  ribbon,  and  her  mother 
gave  her  7 ;  how  many  yards  had  Minerva  then  ? 

40.  There  were  7  boys  sitting  on  one  bench,  and  8 
on  another  •  how  many  boys  were  on  both  ? 

41.  There  were  7  boys  at  play,  and   9   other  boys 
joined  them  ;  how  many  boys  were  in  all  2 

42.  if  I  have  8  cents  in  one  hand,  and  7  cents  in  the 
other,  how  many  have  I  in  both  hands? 

43.  If  Mary  has  8  peaches,  and  Margaret  has  9,  how 
many  have  both  ? 

44.  Sally  gave  9  cents  for  some  thread,  and  7  cents 
for  some  needles ;  how  much  did  the  needles  and 
thread  cost  ? 

45.  Charles  has  9  marbles,  and  Albert  has  5 ;   how 
many  marbles  have  Charles  and  Albert  together  ? 

46.  9  birds  were  in  a  tree,  and  6  were  on  the  ground ; 
how  many  birds  in  all  ? 

47.  Sarah  gave  9  cents  for  cinnamon,  and  7  cents  for 
raisins ;  how  many  cents  did  both  cost  ? 

48.  George  shot  9  pigeons,  and  James  shot  8 ;  how 
many  did  both  shoot  ? 

49.  Hussel  caught  7  fish,  and  Robert  caught  5 ;  how 
many  did  both  catch  ? 

50.  In  one  field  there  are  8  horses,  and  in  another 
there  are  9  ;  how  many  are  there  in  both  ? 


LESSON     III. 

How  many  are  10  and  2  ?  10  and  3  ?  10  and  4  ? 

10  and  5  ?      10  and  6  ?  10  and  7  ?  10  and  9 1 
10  and  8  ?     10  and  10  ? 

How  many  are  2  and  2  ?  2  and  12  ?  2  and  22  ? 

2  and  32 '?     2  and  42  ?  2  and  52  ?  2  and  62  ? 

2  and  72?      2  and  82?  2  and  92  ? 


12  ADDITION. 

3.  How  many  are  3  and  3  ?     3  and  13  ?     3  and  23  ? 
3  and  33  ?     3  and  43  ?     3  and  53  ?     3  and  63  ? 

3  and  73  ?     3  and  83  ?     3  and  93  ?     96  and  4  ? 

4.  How  many  are  4  and  4  ?     4  and  14  ?     4  and  24  ? 

4  and  34  ?     4  and  44  ?     4  and  54  ?     4  and  64  ? 

4  and  74  ?     4  and  84  ?     4  and  94  ?     98  and  2  ? 

5.  How  many  are  5  and  5  ?     5  and  15  ?     5  and  25  ? 

5  and  35*?     5  and  45  ?     5  and  55  ?     5  and  65  ? 
5 -and  75  ?     5  and  85  ?     5  and  £5  ? 

6.  How  many  are  6  and  6  ?     6  and  16  ?     6  and  26  ? 

6  and  36  ?     6  and  46  ?     6  and  56  ?     6  and  66  ? 

6  and  76  ?     6  and  86  1     6  and  96  ? 

7.  How  many  are  7  and  7  ?     7  and  17  ?     7  and  271 

7  and  37  ?     7  and  47  ?     7  and  57  ?     7  and  67  ? 

7  and  77  ?     7  and  87  ?     7  and  97  ? 

8.  How  many  are  8  and  8  ?     8  and  18  ?     8  and  28 \ 

8  and  38  ?      8  and  48  ?     8  and  58  ?     8  and  68  ? 

8  and  78  ?     8  and  88  ?     8  and  98  ? 

9.  How  many  are  9  and  9  ?     9  and  19  ?     9  and  29  ? 

9  and  39  ?     9  and  49  2     9  and  59  ?     9  and  69  ? 
9  and  79  ?     9  and  89  3     9  and  99  ? 

10.  How  many  are  10  and  11  ?     10  and  21  ?     10  and 

31  ?     10  and  41  ?     10  and  51  ?     10  and  61 2     10 
and  71  ?     10  and  81  ?     10  and  91  ? 

1 1.  How  many  are  10  and  12  2     10  and  22  •?     10  and 

32  ?     10  and  42  ?     10  and  52  ?     10  and  62  ?     10 
and  72  ?     10  and  82  ?     10  and  92  ? 

12.  How  many  are  10  and  4  ?     10  and  14  ?     10  and 
24  ?     10  and  34  ?     10  and  44  ?     10  and  54  ?     10 
and  64  ?     10  and  74  ?     10  and  84  ?     10  and  94  ? 

13.  How  many  are  11  and  3  ?     11  and  13  ?     11  and 
23?     11  and  33?     11  and  43  ?     11  and  53  ?     11 
and  63  ?     11  and  73  ?     11  and  83  ?     11  and  93  ? 

14.  How  many  are  11  and  4  ?     11  and  14  ?     11  and 
24?     11  and  34?     11  and  44?     11  and  54  ?     11 
and  64  ?     11  and  74  ?     11  and  84  ?     11  and  94  ? 

15.  How  many  are  10  and  5  ?     10  and  15  '?     10  and 


ADDITION. 


13 


35  ?     10  and  45  ?     10  and  55  ?     10  and  65  ?     10 
and  75  ?     10  and  85  ?     10  and  95  ?     10  and  25  2 

16.  How  many  are  11  and  5  ?     11  and  15  ?     11  and 

25  ?     11  and  35  ?     11  and  45  ?     11  and  55  ?     11 
and  65  ?     11  and  75  ?     11  and  85  ?     11  and  95  ? 

17.  "What  is  the  sum  of  3  and  8  ?     3  and  18  ?     3  and 
28  ?     3  and  38  ?     3  and  48  ?     3  and  58  2     3  and 
68  ?     3  and  78  ?     3  and  88  ?     3  and  98  ? 

1 8.  What  is  the  sum  of  8  and  4  ?     8  and  14  ?     8  and 
24  ?      8  and  34  ?     8  and  44  ?     8  and  54  ?     8  and 
64  ?     8  and  74  ?     8  and  84  ?     8  and  94  ? 

19.  What  is  the  sum  of  7  and  5  ?     7  and  17  ?     7  and 
27  ?     7  and  37  ?     7  and  47  ?     7  and  57  ?     7  and 
67  ?     7  and  77  ?     7  and  87  ?     7  and  97  ? 

20.  What  is  the  sum  of  8  and  6  ?     8  and  16  ?     8  and 

26  2     8  and  36  ?     8  and  46  ?     8  and  56  ?     8  and 
66  ?     8  and  76  ?     8  and  86  ?     8  and  96  ? 


LESSON     IY. 


I. 

8 

and 

9 

are 

how 

many? 

2. 

11 

and 

7 

are 

how 

many  ? 

3- 

10 

and 

9 

are 

how 

many  ? 

4- 

7 

and 

14 

are 

how 

many  ? 

5- 

6 

and 

12 

are 

how 

many? 

6. 

9 

and 

15 

are 

how 

many? 

7. 

11 

and 

18 

are 

how 

many  ? 

8. 

15 

and 

12 

are 

how 

many  ? 

9- 

14 

and 

13 

are 

how 

many  ? 

10. 

1G 

and 

14 

are 

how 

many  ? 

n. 

21 

and 

12 

are 

how 

many  ? 

12. 

24 

and 

13 

are 

how 

many  ? 

J3- 

25 

and 

15 

are 

hew 

many  ? 

14. 

27 

and 

13 

are 

how 

many  ? 

15. 

23 

and 

17 

are 

how 

many  ? 

14:  ADDITION. 

1 6.  29  and  11  are  how  many? 

17.  30  and  20  are  how  many? 

1 8.  34  and  15  are  how  many? 

19.  32  and  18  are  how  many? 

The  Sign  of  Addition  is  +,  and  is  called  plus. 
When  +  is  placed   between  two  numbers,  it  denotes  that, 
they  are  to  be  added  together. 

The  Sign  of  Equality  is  =,  and  is  read  equals,  or  equal  to. 
When  =  is  placed  between  two  numbers,  it  denotes  that 
they  are  equal  to  each  other. 

Thus,  2  +  3—5,  is  read  two  plus  three  equals  jive. 
#  *  4-  #  *  *    —    *   *  *   *  # 

20.  33  +  44  are  how  many  ? 

21.  35  H-  15  are  how  many? 

22.  36  4-  12  are  how  many  ? 

23.  40  4-  36  are  how  many  ? 

24.  40  4-  29  are  how  many  ? 

25.  44  4-  20  are  how  many  ? 

26.  48  4-  32  are  how  many  ? 

27.  45  4-  35  are  how  many  ? 

28.  4  4-  8  4-  6  =  what  number  ? 

29.  84-24-7  =  what  number  ? 

30.  10  4-  T  4-  3  =  what  number  ? 

31.  12  4-  10  4-  9  =  what  number? 

32.  15  4-  12  4-  6  =  what  number? 

33.  18  4-  4  4-  10  =  what  number? 

34.  24  4-  16  4-  12  =  what  number 

35.  22  +  33  4-  H  =  what  number  ? 

36.  15  4-  16  4-  2  =  what  number? 

37.  28  4-  12  4-  15  =  what  number  ? 

38.  46  4-  24  -f-  19  =  what  number  ? 

39.  12  +  84-64-4=  what  number  ? 

40.  24  4-  10  4-  6  4-  12  =  what  number? 

41.  22  4-  32  4-  6  4-  10  =  what  number  ? 

42.  37  4-  23  4-  15  =  what  number  ? 

43.  62  4-  26  4-  12  +  8  =  what  number  ? 


ADDITION.  15 


LESSON     Y. 

1.  Three  boys,  James,  Joseph,  and  Jacob,  gave  some 
money  to  a  beggar;  James  gave  him  6,  Joseph  8, 
and  Jacob  10  cents ;  how  many  cents  did  all  give  him  ? 

2.  Gave  8  cents  to  John,  4  cents  to  Morgan,  and  2 
cents  to  Samuel ;  how  many  cents  did  all  receive  ? 

3.  Henry  has  3  marbles,  Harvey  has  10,  and  Charles 
has  7 ;  how  many  marbles  have  all  ? 

4.  Gave  7  nuts  to  one  boy,  6  to  another,  and  7  to  an- 
other ;  how  many  nuts  did  I  give  to  the  three  boys  ? 

5.  Bought  a  basket  of  strawberries  for  7  cents,  a  bas- 
ket of  cherries  fur  4  cents,  and  a  basket  of  plums 
for  8  cents;  how  many  cents  did  all  cost? 

6.  Lydia  has  9  pinks,  Mary  10,  and  Ann  7;   how 
many  pinks  have  all? 

7.  Bought  a  knife  for  14  cents,  and  a  ball  for  12 
cents;  how  much  did  both  cost? 

8.  Gave  18  cents  for  an  arithmetic,  2  for  a  pencil, 
and  10  for  a  slate ;  how  much  did  all  cost  ? 

9.  James  had  12  cents,  and  his  mother  gave  him  13 
more  ;  how  many  had  he  then  2 

10.  Robert  shot  9  birds,  Richard  shot  11,  and  James 
shot  12  ;  how  many  did  all  shoot  \ 

11.  A  boy  bought  a  pound  of  butter  for  44  cents,  a 
pound  of  meat  for  20  cents,  and  a  bunch  of  lettuce 
for  7  cents ;  how  many  cents  did  all  cost  ? 

12.  Bought  a  pound  of  raisins  for  10  cents,  a  pound 
of  candy  for  12  cents,  and  a  pound  of  cinnamon 
for  15  cents ;  how  much  was  the  whole  cost  ? 

13.  John  had  20  marbles,  Matthew  9,  and  Morgan 
12  ;  how  many  had  they  in  all  ? 

14.  James  bought  a  pigeon  for  9  cents,  a  robin  for  10 
cents,  and  a  squirrel  for  12  cents ;  how  much  did 
all  cost  ? 

15.  A   lady   bought  some  pins   for  15  cents,  some 


10  ADDITION. 

thread  for  10  cents,  and  some  lace  for  18  cents; 
how  many  cents  did  all  these  articles  cost  ? 

1 6.  A  gentleman  bought  a,  hat  for  6  dollars,  a  vest 
for  5  dollars,  and  a  coat  for  20  dollars ;  how  many 
dollars  did  he  pay  for  all  ? 

17.  A  man  bought  a  watch  for  40  dollars,  a  chain  for 
15  doJars,  and  a  gold  pen  for  5  dollars;   how 
much  did  he  pay  for  these  three  articles  ? 

1 8.  Jackson  gave  25  cents  to  his  sister,  and  23  to  his 
mother;  how  many  cents  did  he  give  away? 

19.  Bought  a  barrel  of  Hour  for  7  dollars,  a  barrel  of 
pork  for  12  dollars,  and  a  barrel  of  fish  for  11 
dollars  ;  how  much  was  the  whole  cost  ? 

20.  Bought  a  horse  for  60  dollars,  a  cow  for  20  dol- 
lars, and  a  colt  for  25  dollars ;  how  much  did  all  cost  ? 

u.  It'  your  father  should  give  you  12  cents,  your 
mother  14  cents,  and  your  sister  4  cents,  how 
many  cents  would  you  then  have  ? 

22.  A  boy  spent  11  cents  for  candy,  9  cents  for  a 
ball,  and  5  cents  for  a  top ;  how  many  cents  did 
he  spend  for  all  ? 

23.  A  man  bought  some  butter  for  57  dollars,  and 
some  molasses  for  23  dollars ;  how  many  dollars 
did  he  pay  for  both  ? 

24.  A  boy  traveled  17  miles  one  day,  and   23   the 
next ;  how  far  did  he  travel  in  the  two  days  ? 

25.  A  lady  bought  a  hat  for  7  dollars,  a  dress  for  9 
dollars,  and  a  gold  watch  for  60  dollars ;   how 
many  dollars  did  all  cost  ? 

26.  A  mechanic  sold  a  wagon  for  57  dollars,  and  a 
sleigh  for  43  dollars ;  how  much  did  he  receive 
for  both  ? 

27.  A  boy  saw  24  pigeons  on  one  tree,  and  36  on  an- 
other ;  how  uiany  did  he  see  in  all  ?  * 

28.  In  a  certain  recitation  21  questions  were  answered 
correctly,  and  9  incorrectly ;  how  many  questionr 
were  asked  during  the  recitation  ? 


ADDITION. 


17 


29.  Gave  87  dollars  for  a  chaise,  2  dollars  for  a  whip, 
and  11  dollars  for  a  buffalo  robe ;  how  much  was 
given  for  all  ? 

30.  If  a  horse  is  worth  60  dollars,  and  a  sleigh  75 
dollars,  what  is  the  value  of  both  ? 

31.  Matthew  is  15  years  old,  Morgan  is  7,  and  Mar- 
tin is  10  ;  what  is  the  sum  of  their  ages  '( 

32.  A  man  bought  a  load  of  hay  for  7  dollars,  a  load 
of  rye  for  36  dollars,  and  a  load  of  wheat  for  57 
dollars ;  how  much  was  the  whole  cost  ? 

33.  A  man  is  48  years  old,  and  his  wife  is  32  years 
old ;  what  is  the  sum  of  their  ages  ? 

34.  A  farmer  bought  a  horse  for  60  dollars,  and  a 
yoke  of  oxen  for  75  dollars  ;  how  much  did  the 
horse  and  oxen  together  cost  ? 

35.  John  gave  11  apples  to  his  brother,  9  to  his  sis- 
ter, and  kept  12  himself;  how  many  apples  had 
he  at  first  ? 

36.  Simeon  hoed  12  rows  of  corn,  Simon  15,  James 
13,  and  John  11 ;  how  many  rows  did  they  to- 
gether hoe  ? 

37.  A  merchant  sold  30  barrels  of  flour  one  week,  37 
the  next  week,  and  33  the  following  week  ;  how 
many  barrels  did  he  sell  during  the  three  weeks? 

38.  A  merchant  sold  a  barrel  of  sugar  for  25  dollars, 
a  barrel  of  rum  for  15  dollars,  and  a  hogshead  of 
molasses  for  23  dollars;  how  much  did  he  receive 
for  all  these  articles  ? 

39.  A  man  bought  a  firkin  of  butter  for  9  dollars,  a 
keg  of  molasses  for  7  dollars,  a  box  of  cheese 
for  4  dollars,  and  a  box  of  raisins  for  5  dollars ; 
how  much  was  the  entire  cost  ? 

40.  A  lady  bought  a  silk  dress  for  48  dollars,  a  muff, 
for  22  dollars,  a  shawl  for  17  dollars,  and  a  pair 
of  gloves  for  1  dollar :  the  entire  cost  is  required. 

2* 


18  SUBTRACTION. 


SUBTRACTION. 

Subtraction  is  the  process  of  finding  the  different « 
between  two  numbers. 

The  Terms  in  Subtraction  are  three,  the  Minuend, 
Subtrahend,  Eemainder. 

1.  The  Minuend  is  the  number  to  be  diminished; 

2.  The  Subtrahend  is  the  number  to  be  subtracted; 

3.  The  Remainder,  or  Difference,  is  the  excess 
of  the  minuend  over  the  subtrahend. 

LESSON     VI. 

1.  If  I  have  3  apples,  and  give  1  of  them  to  Richard, 
how  many  shall  I  have  left  ? 

ANALYSIS.— If  I  have  3  apples,  and  give  1  to  Richard,  I 
shall  have  remaining  the  difference  between  3  apples  and 
1  apple,  which  is  2  apples. 

2.  William    had  4  chestnuts,   and    gave    1    to   his 
brother ;  how  many  had  he  left  ? 

3.  Martha  had  5  books,  and  on  her  way  to  school, 
lost  one  of  them ;  how  many  had  she  left  ? 

4.  Cornelia  had  0  apples,  and  gave  1  to  her  brother ; 
how  many  had  she  left  ? 

5.  Rachel  had  10  pins,  and  lost  1  of  them ;   how 
many  had  she  left  ? 

6   Martha  had  12  pears,  and  gave  2  to  Elizabeth  ; 
how  many  had  she  left  ? 

7.  Jane  had  5  canary-birds,  and  gave  2  of  them  to 
Eliza ;  how  many  had  Jane  left  ? 

8.  James  had  6  apples,  and  gave  2  away:  how  many 
had  he  remaining  ? 

9.  Cornelia  learned  12  letters  yesterday,  and  has  for- 
gotten 3  of  them;  how  many  does  she  remember? 

10.  James  had  10  marbles,  and  lost  3  ;  how  many 
had  he  left  * 


SUBTRACTION.  19 

ii.  Mary  found  9  roses  on  her  bush,  and  picked  off 
4  of  them  ;  how  many  remained  on  the  bush  ? 

12.  How  many  are  4  less  2? 

13.  How  many*  are  5  less  3? 

14.  How  many  are  7  less  3  ? 

15.  How  many  are  9  less  4? 

1 6.  How  many  are  9  less  3? 

1 7.  How  many  are  9  less  7  ? 

1 8.  How  many  are  9  less  5? 

19.  How  many  are  11  less  4? 

20.  How  many  are  10  less  4  ? 

21.  How  many  are  11  less  5? 

22.  How  many  are  14  less  4? 

23.  How  many  are  8  less  5  ? 

24.  How  many  are  13  less  3  ? 

25.  How  many  are  14  less  5  ? 

26.  How  many  are  17  less  7? 

27.  How  many  are  15  less  5  ? 

28.  How  many  are  13  less  10  ? 

29.  How  many  are  23  less  3  ? 

30.  How  many  are  27  less  7  ? 

The  Sign  of  Sufttraction  is  — ,  and  is  called  minus. 

When  —  is  placed  between  two  numbers,  it  indicates  that 
the  number  on  the  right  is  to  be  subtracted  from  the  number 
on  the  left.  Thus,  7—5=2,  indicates  that  5  is  to  be  subtracted 
from  7,  and  that  the  Remainder,  or  Difference,  is  2 ;  and  is 
read  7  minus  5  equals  2. 


31- 

8  - 

5 

=  how 

many  ? 

32- 

9  - 

7 

—  how 

many  ? 

33- 

10  - 

8 

—  how 

many  ? 

34- 

11  - 

8 

=  how 

many  ? 

35- 

12  - 

0 

—  how 

many  ? 

36. 

13  - 

8 

=  how 

many  ? 

37- 

14  - 

8 

=  how 

many  ? 

38. 

18  — 

8 

=  how 

many? 

39- 

22  — 

12 

=  how 

many  ? 

40. 

24  - 

14 

=  how 

many  ? 

20  SUBTRACTION. 

41.  12  -      4  =  how     many? 

42.  28  —     8  —  how     many  ? 

43.  20  —     5  =  how     many  ? 

44.  20  —     8  =  'how     many  ? 

45.  20  —    9  =  how     many  ? 

46.  20  —    7  =  how     many  ? 

47.  20  —  10  =  how     many? 

48.  20  —  15  —  how     many  ? 

49.  24  —  10  =  how     many  ? 

50.  25  —  10  4-  5  =  what    number  ? 

51.  26  —  10  4-  4  =  what     number? 

52.  28  —  10  4-  2  =  what     number? 

53.  27  —  10  4-  5  =  what     number  ? 

54.  29  —  10  4-  6  =  what     number  ? 

55.  32  —  10  4-  8  =  what     number  ? 

56.  34  —  10  4-  7  =  what     number? 
57-  36  —  10  4-  8  -  what     number? 

58.  35  —  10  4-  4  =  what     number? 

59.  ,     37  —  10  4-  7  —  what     number  ? 

60.  38  —  10  4-  8  =  what     number? 

61.  39  — 10  4- 9  =  what  number?!  70.  52— 22  + 10=whatnumberf 

62.  47  —  1 04- 6  =  what  number  ?!  71.  54—  34+  1 1=  what  number? 
63.40  — 12  4- 9  =  what  number?  72.  56— 46 +  12= what  number? 
64.  42  —  20  4-7  =  what  number?  j  73.  57~  27  +  14  =  what  number? 
65.45  —  204-5= what  number  ?  j  74.  58—48+    9  =  what  number  ? 

66.  46  — 20  4- 6  =  what  number?!  75.  62— 30 +  10= what  number? 

67.  47  — 20  4- 8  =  what  number?  j  76.  65— 40  + 15=what  number? 
68.47  —  3  7  4- 4= what  number? :  77.  68— 48  +  16  =  whatnumber? 
69.  49  — 19  4- 9  =  what  number?!  78.  74— 34 +  15  =  what  number? 

79.  Gave  7  cents  for  a  spool  of  thread,  and  4  cents 
for  a  lemon  ;  how  much  more  did  the  thread  cost 
than  the  lemon  ? 

80.  Paid  18  cents  for  a  pound  of  butter,  and  8  cents 
for  a  pound  of  meat ;  how  much  more  was  paid 
for  the  butter  than  for  the  meat  ? 

81.  James  bought  18  candles,  and  gave  John  7  of 
them  ;  how  many  had  he  left  ? 


SUBTRACTION.  21 

82.  Sold  a  quantity  of  wool  for  27  dollars,  and  re- 
ceived in  part  payment  a  barrel  of  flour  worth  5 
dollars ;  how  many  dollars  remain  due  ? 

83.  James  has  27  marbles,  and  John  has  17;  how 
many  more  has  James  than  John  ? 

84.  Harry  is  15  years  old,  and  Charles  is  9  years  old  ; 
how  many  years  older  is  Harry  than  Charles  ? 

85.  A  teacher  being  asked  how  many  pupils  he  had, 
answered  that  he  usually  had  37,  but  at  present 
he  had  only  2-7 ;  how  many  were  absent  ? 

86.  A  man  purchased  a  watch   for   37  dollars,  but 
found  he   had   only  24  dollars  with  him ;   how 
much  must  he  borrow  to  pay  the  balance  ? 

87.  Mr.  A  has  94  sheep,  and  B  has  44;  how  many 
more  sheep  has  A  than  B  ? 

88.  Morgan  gave   23  cents  for   some  cake,  and  14 
cents  for  some  cinnamon ;   how  much  more  did 
the  cake  cost  than  the  cinnamon  ? 

89.  Michael  had  29  cents,  and  lost  14;   how  many 
had  he  left  ? 

90.  In  a  certain  recitation  47  questions  were  asked, 
and  9  of  them  were  answered  incorrectly ;  how 
many  were  correctly  answered  ? 

91.  A  man  sold  23  sheep  from  a  flock  consisting  of 
93  ;  how  many  sheep  remained  ? 

92.  Mr.  B  bought  a  horse  for  35  dollars,  and  sold  it 
for  46  dollars  ;  how  much  did  he  gain  ? 

93.  A  cow  was  bought  for  25  dollars,  and  sold  for  19 
dollars ;  how  much  was  the  loss  ? 

94.  A  merchant  bought  a  quantity  of  goods  for  95 
dollars,  but  being  damaged  was  obliged  to  sell 
them  for  80  dollars  ;  how  much  did  he  lose  ? 

95.  The  minuend  is  57,  the  subtrahend  is  27 ;  what 
is  the  remainder  ? 

96.  The  minuend  is  67,  the  remainder  is  20 ;  what  is 
the  subtrahend  ? 

97.  The  subtrahend  is  12,  the  remainder  is  18 ;  what 
is  the  minuend  ? 


22  ADDITION     AND     SUBTRACTION. 

LESSON     VII. 

ADDITION  AND  SUBTRACTION  COMBINED. 

1.  James  has  7  chestnuts,  and  Mary  has  4;  how  many 
more  has  James  than  Mary ;  and  how  many  have 
both  ? 

ANALYSIS. — If  James  has  7  chestnuts,  and  Mary  has  4, 
James  has  as  many  more  than  Mary  as  the  difference  be- 
tween 7  chestnuts  and  4  chestnuts,  which  is  3  chestnuts. 
Together  they  have  7  chestnuts  and  4  chestnuts,  which  are 
11  chestnuts. 

2.  Bought  a  barrel  of  fish  for  8  dollars,  and  some 
quinces  for  3  dollars ;  how  much  more  did  the  fish 
cost  than  the  quinces  ?   What  was  the  cost  of  both  ? 

3.  Gave  15  dollars  for  a  cow  and  6  dollars  for  a  sheep ; 
how  much  more  was  given  for  the  cow  than  for  the 
sheep  ?     How  much  was  given  for  both  ? 

4.  Phineas  gave  50  cents  for  a  grammar,  and  25  cents 
for  an  arithmetic ;  how  much  was  the  cost  of  both  ? 
How  much  did  one  cost  more  than  the  other  ? 

5.  Paid  15  dollars  for  a  barrel  of  rum,  and  6  dollars 
for  a  barrel  of  flour;  how  much  was  the  cost  of 
both  ;  and  how  much  more  did  the  rurn  cost  than 
the  flour  ? 

6.  Sold  a  firkin  of  butter  for  10  dollars,  a  cheese  for  5 
dollars,  and  received  in  part  payment  a  barrel  of 
flour  worth  6  dollars  ;  how  much  remains  due  ? 

7.  James  gave  12  cents  for  oranges,  15  cents  for  cake, 
and  had  13  cents  remaining ;  how  much  had  he  at 
first? 

8.  Mary  bought  a  comb  for  10  cents,  a  spool  of  thread 
for  12  cents,  and  a  paper  of  needles  for  8  cents; 
she  handed  the  clerk  37  cents ;  how  much  change 
ought  she  to  receive  ? 

Q.  A  man  sold  a  cow  for  20  dollars,  a  calf  for  4  dol- 
lars, and  a  sheep  for  3  dollars ;  and  in  part  pay- 
ment received  a  wagon  worth  17  dollars;  how 
much  remains  due  ? 


ADDITION    AND    S'U-BTE  ACTION.  23 

10.  A  lady  bought  a  ribbon  for  24  cents,  some  tape 
for  8  cents,  and  some  thread  for  12  cents ;  she 
had  only  60  cents  ;  how  much  remained  after  she 
paid  for  these  articles  ? 

11.  Stephen,  at  one  game  of  marbles,  won  4,  and  at 
another  he  lost  6,  and  then  had  only  8  remaining ; 
how  many  had  he  at  first  ? 

1 2.  Sampson  having  9  apples,  gave  4  to  his  mother, 
and  3  to  his  sister ;  for  his  generosity  his  father 
gave  him  13  more;  how  many  had  he  then  ? 

13.  A  man  bought  some  cloth  for  12  dollars,  and  sold 
it  for  18  dollars;  how  much  was  his  gain  ? 

14.  A  farmer  bought  a  horse  for  63  dollars,  and  ex- 
changed it  for  a  yoke  of  oxen  ;  these  he  sold  for  87 
dollars ;  how  much  did  he  gain  by  the  operation  ? 

15.  A  man  bought  a  yoke  of  oxen  for  97  dollars,  their 
services  earned  for  him  40  dollars,  and  their  keep- 
ing cost  him  13  dollars ;  he  then  sold  them  for 
80  dollars  ;  how  much  did  he  gain  ? 

1 6.  A  box  of  raisins  was  bought  for  3  dollars,  a  firkin 
of  butter  for  15  dollars,  and  were  both  sold  for  20 
dollars ;  how  much  was  gained  '( 

17.  A  farmer  sold  a  cow  for  29  dollars,  which  was  5 
dollars  more  than  she  cost ;  how  much  did  she  cost  ? 

1 8.  A  drover  bought  some  sheep  for  40  dollars,  some 
cattle  for  130  dollars,  and  sold  them  all  for  200 
dollars  ;  how  much  was  his  gain  ? 

19.  A  jeweller  bought  a  watch  for  20  dollars,  a  chain 
for  10  dollars,  a  key  for  2  dollars,  and  sold  them 
all  for  42  dollars ;  how  much  did  he  gain  by  the 
bargain  ? 

20.  24  +  12+   9= how  many? 

21.  10  +  30  + 1 5 = how  many  ? 

22.  14+16  +  ll  =  how  many? 

23.  36+   9-12=howmany? 

24.  38  +  22— 15— how  many? 

25.  43  +  37— 20r=how  many  ? 

26.  13  +  26— 25 -how  many  ? 


24  ADDITION     AND     S  U  B  T  K  A  6  T  I  O  Bf . 

27.  44— 20  +  10— 12=how  many? 

28.  27  +  23—20+   2  =  howmany? 

29.  15  +  25— 30  +  15  =how  many  ? 

30.  20  +  40—30+  10  =  hovv  many  ? 

31.  A  boy  bought  a  ball  for  6  cents;  for  how  much 
must  he  sell  it  to  gain  4  cents  ? 

32.  A  merchant  bought  a  hogshead  of  molasses  for  47 
dollars,  and  paid  3  dollars  for  cartage  ;  for  how 
much  must  he  sell  it  to  gain  12  dollars  ? 

33.  A  grocer  bought  a  hogshead  of  sugar  for  30  dol- 
lars ;  for  what  must  he  sell  it  to  gain  18  dollars  ? 

34.  A  drover  bought  sheep  as  follows  :  of  one  man  he 
bought  24,  of  another  8,  and  of  another  22  :    he 
then  sold  20  of  them ;  how  many  remained  unsold  ? 

35.  A  watch  cost  40  dollars;  how  must  it  be  sold  to 
gain  13  dollars? 

36.  Four  boys  bought  a  melon  ;  one  gave  3  cents,  an- 
other 4,  another  8,  and  the  other  6 ;  how  much 
did  they  pay  for  the  melon  ? 

37.  Mary  bought  16  plums  at  one  store,  and  13  at 
another ;  on  her  way  home  she  ate  11  of  them  ; 
how  many  had  she  left  ? 

38.  Matthew  had  9  nuts,  Mary  gave  him  10  more, 
and  John  gave  him  enough  to  make  his  number 
39  ;  how  many  did  John  give  him  ? 

39.  A  farmer  had  25  sheep  in  one  field,  and  15  in 
another ;  he  then  bought  as  many  more  as  made 
his  number  56 ;  how  many  did  he  buy  ? 

40.  John  has  34  marbles,  and  Albert  25  ;  how  many 
have  both  ?     How  many  more  has  John   than 
Albert  ? 

41.  A  butcher  has   57  sheep,  and  44  lambs;    how 
many  more  sheep  has*  he  than   lambs  ?     How 
many  sheep  and  lambs  together  ? 

42.  Paid  97  dollars  for  a  quantity  of  sugar,  and  43 
dollars  for  some  molasses ;  how  much  more  did 
the  sugar  cost  than  the  molasses  ?     How  much, 
did  both  cost  ?. 


MULTIPLICATION. 


MULTIPLICATION. 

Multiplication  is  the  process  of  taking  one  num 
ber  as  many  times  as  there  are  units  in  another. 

Multiplication  is  also  a  method  of  finding  the  sum 
of  several  equal  numbers. 

The  Terms  in  Multiplication  are,  the  Multiplicand, 
Multiplier,  and  Product. 

1.  The  Multiplicand  is  the  number  to  be  taken  ; 

2.  The  Multiplier  is  the  number  which  shows  how 
many  times  the  multiplicand  is  to  be  taken; 

3.  The  Product  is  the  result  obtained. 


L 

ESS 

ON 

y 

III. 

I. 

Two 

times 

1 

are 

how 

many  ? 

2. 

Two 

times 

2 

are 

how 

many  ? 

3- 

Two 

times 

3 

are 

how 

many  ? 

4- 

Two 

times 

4 

are 

how 

many  ? 

Two 

times 

5 

are 

how 

many  \ 

6. 

Two 

times 

6 

are 

how 

many  ? 

7. 

Two 

times 

7 

are 

how 

many  ? 

8. 

Two 

times 

8 

are 

how 

many  ? 

9- 

Two 

times 

9 

are 

how 

many  ? 

10. 

Two 

times 

10 

are 

how 

many  ? 

u. 

Two 

times 

11 

are 

how 

many  ? 

12. 

Two 

times 

12 

are 

how 

many  ? 

13.  What  will  2  oranges  cost,at  3  cents  each  ? 

ANALYSIS. — If  1  orange  cost  3  cents,  2  oranges  will  cost 
two  times  3  cents ;  which  are  6  cents. 

14.  What  will  2  peaches  cost,  at  2  cents  each  ? 

15.  What  will  2  apples  cost,  at  3  cents  each  ? 

1 6.  What  will  2  pine-apples  cost,  at  8  cents  each  ? 

17.  What  will  2  pencils  cost,  at  8  cents  each  ? 

1 8.  What  will  2  quails  cost,  at  11  cents  each ! 

19.  What  will  2  primers  cost,  at  12  cents  each  ? 

2 


MULTIPLICATION. 


2O. 
21. 
22. 

23- 

24- 

25- 

26. 

27- 
28. 
29. 

31- 
32. 
33- 

34. 
35- 
36. 
37- 
38. 

39- 

40. 

42. 
43- 
44- 

45- 
46. 

47- 
48. 

49- 

50. 


What  will 
What  will 
What  will 
Three 
Three 
Three 
Three 
Three 
Three 
Three 
Three 
Three 
Three 
Three 
Four 
Four 
Four 
Four 
Four 
Four 
Four 
Four 
Four 
Four 


*2  citrons  cost,  at  10  cents  each  ? 
2  tops  cost,  at  9  cents  each  ? 
2  lemons  cost,  at  4  cents  each  ? 


times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 


2 
3 
4 
5 
6 
7 
-8 
9 

10 

11 

12 

3 

4 

5 

6 

7 

8 

9 

10 
11 
12 


are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 
are 


how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 
how 


many  ? 
many  ? 
many  ? 
many? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many? 
many? 
many  ? 
many? 
many  \ 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 
many  ? 


What  will  3  quarts  of  cherries  cost,  at  6  cents  a 

quart  ? 

What  will 

What  will 

What  will 

What  will 

quart  ? 

What  will 

yard  ? 

What  will 


3  lead  pencils  cost,  at  5  cents  each  ? 
3  quarts  of  milk  cost,  at  4  cents  a  quart  ? 
3  yards  of  ribbon  cost,  at  7  cents  a  yard  ? 
quarts  of  chestnuts  cost,  at  6  cents  a 


ounce  « 
What  will 
an  ounce  ? 


4  yards  of  .edging  cost,  at  5  cents  a 

3  ounces  of  snuff  cost,  at  8  cents  an 

4  ounces  of  cinnamon  cost,  at  7  cents 


ULTIPLIC ATION. 


27 


52.  What  will  3  pounds  of  cheese  cost,  at  10  cents  a 
pound  ? 

53.  What  will  4  sheets  of  wadding  cost,  at  8  cents  a 
sheet  ? 

54.  What  will  3  yards  of  calico  cost,  at  11  cents  a 
yard  ? 

55.  What  will  4  skeins  of  silk  cost,  at  9  cents  a  skein  ? 

56.  What  will  3  yards  of  ribbon  cost,  at  12  cents  a 
yard  ? 

57.  What  will  4  pounds  of  starch  cost,  at  12  cents  a 
pound  ? 

58.  What  will  4  candlesticks  cost,  at  11  cents  each  ? 

59.  What  will  4  tops  cost,  at  10  cents  each  ? 

60.  What  will  5  apples  cost,  at  4  cents  each  ? 

TJie  Sign  of  Multiplication  is  x ,  and  is  read  multi- 
plied by,  or  times. 

When  x  is  placed  between  two  numbers,  it  denotes  that 
either  is  to  be  multiplied  by  the  other.  Thus,  4x5=20,  de- 
notes that  4  is  to  be  multiplied  by  5  (or  5  by  4),  and  that  the 
product  is  20 ;  and  is  read  4  times  5  equals  20,  or  4  multiplied 
by  5  equals  20. 


61.  5  x    6—  how  many  ? 
62.  5  x    7—  how  many  ? 
63.  5  x    9—  how  many  ? 
64.  5  x    8=  how  many  ? 
65.  5  x    5=  how  many  ? 
66.  5  x  10=  how  many  ? 
67.  5  x  12=how  many  ? 
68.  5  x  ll=how  many  ? 
69.  6  x    6=how  many  ? 
70.  6x   8=  how  many? 
71.  6x    7=howmany? 

72.  6  x  10=how  many  ? 
73.  6x    9  —  how  many? 
74.  6  x  12=  how  many  ? 
75.  0  x  ll=liow  many  ? 
76.  7x    6=howmany? 
77.  7x    8=howmany? 
78.  7  x    7=how  many  ? 
79.  7x  10=how  many  ? 
80.  7x    9=howmany? 
8  1.  7x  12=how  many  ? 
82.  7xll=how  many  ? 

83.  What  will  5  barrels  of  flour  cost,  at  6  dollars  a 
barrel  ? 

84.  What  will  5  bushels  of  potatoes  cost,  at  5  dimes 
a  bushel  ? 


28  MULTIPLICATION. 

85.  What  will  6  primers  cost,  at  6  cents  each  ? 

86.  What  will  5  barrels  of  fish  cost,  at  7  dollars  a 
barrel  ? 

87.  What  will  6  pounds  of  mutton  cost,  at  7  cents  a 
pound  ? 

88.  What  will  5  barrels  of  sugar  cost,  at  12  dollars  a 
barrel  \ 

89.  What  will  6  pounds  of  sturgeon  cost,  at  10  cents 
a  pound  ? 

90.  What  will  G  pounds  of  almonds  cost,  at  12  cents 
a  pound  ? 

91.  What  will  5  barrels  of  pork  cost,  at  $10  a  barrel  ? 

92.  What  will  6  pounds  of  candles  cost,  at  9  cents  a 
pound  ? 

93.  What  will  5  coats  cost,  at  9  dollars  each  ? 

94.  What  will  6  handkerchiefs  cost,  at  1 1  cents  each  \ 

95.  What  will  6  inkstands  cost,  at  8  cents  each  ? 

96.  What  will  7  lamps  cost,  at  9  dimes  each  ? 

97.  What  will  7  plows  cost,  at  8  dollars  each  ? 

98.  What  will  7  boxes  of  caps  cost,  at  10  cents  a  box  ? 

99.  What  will  7  quires  of  paper  cost,  at  12  cents  a 
quire  ? 

100.  What  will  7  letter-folders  cost,,  at  11  cents  each  ? 


IOI. 

Eight 

times 

8 

are 

how 

many  ? 

102. 

Eight 

times 

10 

are 

how 

many  'i 

103. 

Nine 

times 

8 

are 

how 

many  ? 

104. 

Eight 

times 

7 

are 

how 

many  ? 

105. 

Nine 

times 

9 

are 

how 

many  ? 

106. 

Eight 

times 

9 

are 

how 

many  ? 

107. 

Nine 

times 

11 

are 

how 

many  ? 

108. 

Eight 

times 

12 

are 

how 

many  ? 

109. 

Nine 

times 

10 

are 

how 

many  ? 

no. 

Eight 

times 

11 

are 

how 

many  ? 

III. 

Nine 

times 

12 

are 

how 

many  ? 

112.    ^ 

Hiat  will 

9  bunc 

hes  c 

>f  ros 

es  cost 

;,  at  9  ce 

bunch  ? 
1 13.  What  will  8  pen-knives  cost,  at  12  cents  each  ? 


MULTIPLICATION.  29 

i  ^4.  What  will  9  bunches  of  grapes  cost,  at  12  cents 
a  buneh  ? 

115.  What  will  11  yards  of  calico  cost,  at  11  cents  a 
yard  ? 

1 1 6.  What  will  10  balls  of  cotton  cost,  at  12  cents  a 
ball  ? 

117.  What  will  11  pounds  of  ginger  cost,  at  12  cents 
a  pound  ? 

1 1 8.  What  will  10  blocks  of  tape  cost,  at  8  cents  a 
block  ? 

119.  What  will  12  yards  of  cloth  cost,  at  12  dimes  a 
yard  ? 

1 20.  What  will  13  pairs  of  boots  cost,  at  $4  a  pair? 


LESSON     IX. 

ADDITION,   SUBTRACTION,  AND  MULTIPLICATION  COMBINED, 

1.  A't  7  cents  each,  what  will  9  pine-apples  cost  ? 

2.  If  the  postage  on  1  letter  is  3  cents,  what  will  be 
the  postage  on  8  letters  ? 

3.  If  it  require  8  yards  of  calico  to  make  1  dress,  how 
many  yards  will  it  require  to  make  7  dresses  ? 

4.  If  John  obtain  2  credit-marks  in  one  day,  how 
many  will  he  have  in  15  days? 

5.  A  man  hired  a  horse  to  ride  12  miles,  at  the  rate 
of  5  cents  a  mile ;  how  much  must  he  pay  ? 

6.  Margaret's  cloak  contains  7  yards  of  merino,  worth 
9  dimes  a  yard ;  what  is  tho  value  of  her  cloak  ? 

7.  If  a  stage-coach  go  9  miles  in  an  hour,  how  far 
will  it  go  in  7  hours  ? 

8.  At  8  dollars  a  week,  how  much  will   5  weeks' 
board  amount  to  ? 

9.  If  the  fare  by  railroad  from  Albany  to  Boston  is  5 
dollars  for  1  person ;  how  much  will  it  be  for  a 
family  of  9  persons  ? 


30  M  U  L  T  I  T  LI  C  A  T  I  O  N  . 

10.  Helen  had  8  rose  bushes,  and  there  were  7  roses 
on  each  ;  how  many  roses  had  she  in  all  ? 

11.  At  3  dimes  a  gallon,  what  will  15  gallons  of 
molasses  cost  ? 

NOTE. — One  dime  =  10  cents. 

12.  There  are  10  rows  of  trees  in  an  orchard,  and  12 
trees  in  each  row ;  how  many  trees  are  there  in 
the  orchard  ? 

13.  A  traveler  meeting  13  beggars,  gave  to  each  of 
them  3  dimes ;  how  many  dimes  did  he  give  to 
all  of  them  ? 

14.  A  woman  bought  11  yards  of  cloth,  and  paid  for 
it  with  butter,  giving  9  pounds  for  a  yard  ;   how 
many  pounds  of  butter  did  it  take  to  pay  for  the 
cloth  ?     How  much  did  the  cloth  cost,  provided 
the  butter  was  worth  10  cents  a  pound '( 

15.  In  a  certain  corn  field  there  are  24  rows,  and  30 
hills  in  each  row ;  how  many  hills  in  the  field  '{ 

1 6.  What  will  40  steel  pens  cost,  at  2  cents  each  ? 

17.  "What  will  8  pairs  of  snuffers  cost,  at  3  dimes  a 
pair? 

1 8.  When  2  dimes  are  paid  for  1  duck,  what  will  be 
the  cost  of  8  ducks  ?  of  10  ducks  ?  of  12  ducks  ? 

19.  When  hay  is  worth  8  dollars  a  ton,  what  is  th< 
value  of  2  tons  ?  of  4  tons  ?  of  3  tons  ?  of  7  tons  ? 
of  5  tons  ?  of  10  tons  ?  of  12  tons  ?  of  14  tons  ? 

20.  At  2  dimes  each,  how  many  cents  will  4  books 
cost  ?    6  books  ?  10  books  ?  12  books  ?  11  books  ? 
7  books  ?  16  books  ?  13  books  ?  14  books  ? 

21.  If  5  cents  will  buy  one  primer,  what  will  be  the 
cost  of  4  primers  ?'  of  6  ?  of  9  ?  of  8  ?  of  10  ? 

22.  6  plates,  at  5  dimes  each,  will  cost  how  much  ? 

23.  At  5  dimes  each,  how  much  will  4  handkerchiefs 
cost?  6?  8?  10?  12?  14?  11?  16? 

24.  At  6  dimes  each,  how  many  cents  will  2  geese 
cost?  4?  5?  8?  10?  12?  9?  7? 


MULTIPLICATION.       -  31 

25.  At  12  cents  each,  bow  much  will  3  candlesticks 
cost  ?     How  much  will  6  ?  5  ?  8  ?  9  ?  10  ?  7  ? 

26.  If  I  pay  5  cents  for  riding  1  mile,  how  much  must 
I  pay  for  riding  7  miles  ?  8  miles  ?  9  ?  6  ?  10  ?  12  ? 

27.  At  7  cents  a  yard,  how  much  will  5  yards  of  rib- 
bon cost?  6  yards?  8  yards?  9  yards?  10  yards? 
12  yards  ? 

28.  If  a  tooth-brush  cost  18  cents,  how  much  will  4 
cost? 

29.  9  turkeys  will  cost  how  much,  at  8  dimes  each? 

30.  At  14  cents  a  quire,  how  much  will  2  quires  of 
paper  cost  ?   3  quires  ?  4  quires  ?  5  quires  ? 

31.  How  much  will  7  pictures  cost,  at  5  cents  each? 
at  6  cents  each  ?  at  8  cents  each  ?  at  10  cts.  each  ? 

32.  How  much  will  8  knives  cost,  at  6  dimes  each  ? 
at  10  dimes  each  ? 

33.  At  10  dimes  each,  how  much  will  4  caps  cost  ? 
5?  6?  8?  9?  12?  14?  17?  19?  21?  25? 

34.  At  40  cents  a  day,  how  much  will  2  days'  work 
amount  to  ?    5  days'  work  ? 

35.  If  one  paper  of  candy  cost  6  cents,  how  much  will 
3  papers  cost?   5  papers?  8  papers?  12  papers? 

36.  At  7  dollars  a  hundred  feet,  how  much  will  4 
hundred  feet  of  cedar  boards  cost  ?     9  hundred 
feet?   10  hundred  feet  ? 

37.  If  1  bushel  of  wheat  cost  60  cents,  how  much 
will  6  bushels  cost  ?   4  bushels  ?  5  bushels  ? 

38.  How  much  will  8  muffs  cost,  at  12  dollars  each  ? 

39.  How  much  will  19  lead  pencils  cost,  at  5  cents 
each  ? 

40.  How  much  will  11  boxes  of  cheese  cost,  at  4  dol- 
lars a  box  ?  at  5  dollars  a  box  ?  at  8  dollars  a  box  ? 

41.  How  much  will  12  barrels  of  pork  cost,  at  5  dol- 
lars a  barrel  ?    at  8  dollars  ?    at  9  dollars  ?    at  10 
dollars  ? 

42.  How  much  will  9  tons  of  hay  cost,  at  13  dollars 
a  ton? 


32  ADDITION,     SUBTRACTION, 

43.  James  is  9  years  old,  and  his  father  is  4  times  as 
old ;  how  old  is  his  father  ? 

44.  Jane's   frock   contains  7  yards  of  silk,  worth  8 
dimes  a  yard ;  what  was  the  value  of  the  silk  ? 
Provided  the  making  cost  2  dollars,  how  much 
was  the  cost  of  her  dress  ? 

45.  If  a  barrel  of  flour  will  serve  12  men  8  days,  how 
long  will  it  serve  1  man  ? 

46.  If  I   earn    12  dollars   in   a  month,  and   spend 
8,  how  much  will  I   have  at  the  end   of   12 
months  ? 

47.  If  I  earn  12  dollars  a  month,  and  pay  25  cents  a 
week  for  washing,  and  2  dollars  a  week  for  board, 
how  much  will  I  have  at  the  end  of  40  weeks  (10 
months)  2 

4.8.  If  I  buy  9  tons  of  hay,  at  12  dollars  a  ton,  and 
sell  6  tons,  at  15  dollars  a  ton,  and  the  3  remain- 
ing tons,  at  10  dollars  a  ton  ;  how  much  shall  I 
gain  ? 

49.  Bought  11  yards  of  broadcloth,  at  4  dollars  a 
yard,  but,  being  damaged,  I  lost  18  dollars  by 
the  sale  of  it ;  how  much  did  I  receive  for  it  ? 

50.  If  I  buy  12  barrels  of  pork,  at  8  dollars  a  barrel, 
and  sell  it  all  for  108  dollars,  how  much  shall  I 
gain  by  so  doing  ? 

51.  A  man  bought  a  horse  for  80  dollars,  paid  2  dol- 
lars a  week  for  his  keeping,  and  received  4  dollars 
a  week  for  his  work ;  at  the  expiration  of  10  weeks 
he  sold  him  for  70  dollars ;    how  much  did  he 
gain? 

52.  For  how  much  must  I  sell  4  barrels  of  wheat 
which  cost  me  8  dollars  a  barrel,  to  gain  8  dol- 
lars ? 

53.  What  is  the  cost  of  9  cows,  at  25  dollars  each  ? 

54.  Provided  a  hunter   should  kill   5  pigeons,  and 
wound  4  at  every  shot,  how  many  would  he  kill 
and  wound  by  shooting  8  times  ? 


AND     MULTIPLICATION.  33 

55.  If  a  man  travel  20  miles  in  a  day,  how  many 
miles  will  he  travel  in  6  days  ? 

56.  How  much  will  8  months'  wages  amount  to,  at 
18  dollars  a  month? 

57.  If  10  men  eat  18  pounds  of  butter  in  1  week,  how 
long  would  it  last  one  man  ? 

58.  If  80  dollars  will  pay  for  4  dinners  for  20  men, 
how  many  dinners  would  it  buy  for  1  man  ? 

59.  Bought  3  yards  of  cloth  for  a  coat,  at  7  dollars  a 
yard,  the  buttons  and  cord  cost  2  dollars,  buckram 
and  wadding,  1  dollar,  paid  for  making  it  6  dol- 
lars ;   for  how  much  must  I  sell  it  to  gain  5 
dollars  ? 

60.  If  IT  men  can  do  a  piece  of  work  in  9  days,  how 
many  days  would  it  take  1  man  to  perform  the 
same  work  ? 

6 1.  Two  men  start  from  the  same  place,  and  travel 
in  opposite  directions,  one  at  the  rate  of  7  miles 
an  hour,  the  other,  9  miles  an  hour;    how  far 
apart  will  they  be  in  2  hours  ? 

62.  Two  men  start  from  the  same  place,  and  travel 
the  same  way,  one  at  the  rate  of  3  miles  an  hour, 
the  other,  8  miles  an  hour;   how  far  apart  will 
they  be  at  the  end  of  8  hours  ? 

63.  Two  men  are  50  miles  apart,  and  approach  esch 
other,  one  at  the  rate  of  2  miles  an  hour,  the 
other,  3  miles  an  hour ;   how  far  apart  will  they 
be  at  the  end  of  5  hours  ? 

64.  If  1  orange  is  worth  4  apples,  how  many  apples 
must  be  given  for  13  oranges  ? 

65.  A  boy  earned  80  cents  a  day,  and  paid  50  cents 
a  day  for  his  board  and  washing;  how  much  had 
he  left  at  the  expiration  of  6  days  ? 

66.  Jane  bought  4  yards  of  silk,  at  2  dollars  a  yard, 
3  shawls,  at  10  dollars  each,  and  some  delaine  for 
10  dollars ;  she  paid  5  ten-dollar  bills ;  how  much 
O'lght  she  to  receive  back? 


l  ADDITION MULTIPLICATION. 

67.  Mary  bought  5  yards  of  silk,  at  8  dimes  a  yard, 
and  8  yards  of  linen,  at  9  dimes  a  yard ;   how 
many  yards  did  she  buy,  and  how  much  did  all 
cost? 

68.  In  a  certain  school  there  are  12  girls,  and  3  times 
as  .many  boys,  less  8  ;   how  many  boys   in  the 
school,  and  how  many  boys  and  girls  together  ?    , 

09.  John  has  7  books,  and  Mary  has  4  times  as  many, 
less  18  ;  how  many  has  Mary,  and  how  many 
have  both  ? 

70.  Albert  has  9  marbles,  Aaron  3  times  as  many, 
less  7,  and  Amos  has  twice  as  many  as  both,  less 

8  ;  how  many  has  each,  and  how  many  have  they 
together  ? 

71.  Perry  worked  for  Elisha  4  days,  at   6  dimes  a 
day;    Elisha  gave  him  7  bushels  of  corn,  at  3 
dimes  a  bushel ;  how  much  was  then  due  Perry  ? 

72.  A  merchant  bought  25  pounds  of  sugar  for  125 
cents,  and   sold    15  pounds  of  it,  at  6  cents  a 
pound,  and  the  remaining  10  pounds,  at  4  cents 
a  pound ;  how  much  did  he  gain  by  so  doing  ? 

73.  If  the  interest  on  1  dollar  for  a  year  is  6  cents, 
how  much  is  the  interest  on  13  dollars  for  the 
same  time  ? 

74.'  What  will  27  pounds  of  beef  cost,  at  4  cents  a 
pound  ? 

75.  When  beef  is  5  cents  a  pound,  and  pork  9  cents, 
how  much  more  will  9  pounds  of  pork  cost  than 

9  pounds  of  beef? 

76.  Mary  bought  35  quarts  of  milk,  and  on  her  way 
home  she  spilled  4  times  2  quarts,  less  3  quarts ; 
how  many  quarts  had  she  remaining  ? 

77.  James  has  9  walnuts,  John  twice  as  many,  less 
8,  and  Joseph  twice  as  many  as  James  and  John, 
4-  7 ;   how  many  has  each,  and  how  many  have 
all? 


DIVISION. 


35 


DIVISION. 

Division  is  the  process  of  finding  how  many  times 
one  number  contains  another.  • 

Also,  of  finding  one  of  the  equal  parts  of  a  number. 

The  Terms  of  Division  are  the  Dividend,  Divisor, 
Quotient,  and  Remainder. 

1.  The  Dividend  is  the  number  to  be  divided  ; 

2.  The  Divisor  is  the  number  to  divide  by  ; 

8.  The  Quotient  is  the  number  of  times  the  divi- 
dend contains  the  divisor,  or  the  value  of  the  required 
part  of  the  dividend  ; 

4.  The  Remainder  is  the  part  of  the  dividend 
which  is  left,  when  the  dividend  does  not  contain  the 
divisor  an  exact  number  of  times.  The  remainder  is 
always  less  than  the  divisor. 

L  E  S  S  O  1ST     X. 

i  .          8     are     how     many     times     2  ? 

ANALYSIS.  —  8  are  as  many  times  2  as  2  is  contained  times  in 
8,  which  are  4  times. 

2.  6     are     how     many     times     2  ? 

3.  4     are     how     many     times     2  ? 

4.  10     are     how     many     times     2  ? 

5.  12     are     how     many     times     2  ? 

6.  14    are     how     many     times     2  ? 

6  are  how  many  times  32 

9  are  how  many  times  3  ? 

9.        12  are  how  many  times  3  ? 

10.  15  are  how  many  times  8? 

11.  18  are  how  many  times  3? 

12.  21  are  how  many  times  3? 

13.  24  are  how  many  times  3? 

14.  16  are  how  .  many  times  2  ? 

15.  18  are  how  many  times  2? 


7. 
8. 


36  DIVISION. 

1 6.  20  are  how  many  times  2? 

17.  22  are  how  many  Jimes  2? 

1 8.  24  are  how  many  times  22 

19.  26  are  how  many  times  2  ? 

20.  •      28     are    how     many     times     2? 

21.  At  2  cents  each,  how  many  apples  can  you  buy 
for  4  cents  3 

ANALYSIS  IST.— If  for  2  cents  I  can  buy  1  apple,  for  4  cents 
I  can  buy  as  many  apples  as  2  cents  is  contained  times  in  4 
cents,  which  are  2  times.  Therefore,  at  2  cents  each,  for  4 
cents  I  can  buy  2  apples. 

ANALYSIS  2D.—  If  2  cents  will  buy  1  apple,  4  cents  will  buy 
as  many  apples  as  2  is  contained  times  in  4,  which  is  2. 

ANALYSIS  3D. —  If  for  2  cents  I  can  buy  1  apple,  for  1  ce-nt  I 
can  buy  one-half  of  an  apple  ;  and  for  4  cents,  4  times  one- 
half,  which  are  4  halves,  or  2  apples. 

22.  At  2  cents  each,  how  many  oranges  can  I  buy  for 
6  cents  ? 

23.  At   2   cents   each,   how  many   peaches   can   be 
bought  for  8  cents  '{ 

24.  At  3  dimes  a  yard,  how  many  yards  of  calico  can 
be  bought  for  12  dimes  ? 

25.  At  3  cents  each,  how  many  lemons  can  be  bought 
for  9  cents  \ 

26.  At  2  cents  a  yard,  how  many  yards  of  tape  can 
be  bought  for  10  cents  ? 

27.  At  2  dimes  a  bushel,  how  many  bushels  of  apples 
may  be  had  for  12  dimes  ? 

28.  How  many  pounds  of  ginger,  at  2  dimes  a  pound, 
may  be  had  for  14  dimes  'i 

29.  How  many  baskets  of  strawberries,  at  3  cents  a 
basket,  can  be  had  for  15  cents  ? 

30.  For  16  dollars,  how  many  yards  of  cloth  can  be 
had,  at  2  dollars  a  yard  ? 

31.  For  18  apples,  how  many  oranges  can  be  bought, 
at  the  rate  of  2  apples  for  1  orange  1 

32.  How  many  primers,   at   2   cents   each,    can   be 
bought  for  24  cents  ? 


DIVISION 


37 


33.  How  many  barrels  of  flour,  at  5  dollars  a  barrel, 
can  be  bought  for  20  dollars  ? 

34.  For  22  dollars,  how  many  sheep  may  be  bought, 
at  2  dollars  each  ? 

35.  How  many  melons  may  be  had  for  18  dimes,  at 
3  dimes  each '( 

36.  At  3  cents  each,  how  many  tops  will  6  cents  buy  ? 

37.  At  3  dimes  a  peck,  how  many  beans  will  $2.10  buy  ? 

38.  At  3  cents  a  mile,  how  far  can  I  ride  for  24  cents  ? 

39.  At  4  dimes  a  bushel,  how  much  rye  will  $1.20  buy  ? 

40.  How  many  books,  at  4  dimes  each,  can  be  bought 
for  20  dimes  ? 

The  Siffii  of  Division  is  -T-,  and  when  placed  between 
two  numbers,  it  denotes  that  the  one  on  the  left  is  to  be 
divided  by  the  one  on  the  right.  Thus,  6-^-3=2,  or  f  —  2  de- 
notes that  6  is  to  be  divided  by  3,  and  that  the  quotient  equals 
2  ;  and  is  read,  6  divided  by  3  equals  2. 


4L     8— 4= how  many  ? 

42.  12— 4=how  many  ? 

43.  16— 4  =  how  many  ? 

44.  10— 5  =  how  many  ? 

45.  15— 5= how  many  ? 

46.  20— 5=how  many  ? 

47.  28— 7=how  many  ? 


48.  32— 4= how  many  ? 

49.  30— 5— how  many  ? 

50.  35— 5= how  many  ? 

51.  36— 4=how  many  ? 

52.  40— 5= how  many  ? 

53.  44— 4  — how  many  ? 

54.  30— 6= how  many  ? 


55.  48  contains  8  how  many  times  ? 

ANALYSIS. — 48  contains  8,  6  times  [because  6  times  8  are  48]. 

56.  24  contains  8  how  many  times  ?     4  ?     12  ?     3  ? 


57- 
58. 

59- 

60. 


contains  9  how  many  times  ? 


6  ? 
3? 

5? 

4? 


3? 

9? 
15? 


54  contains  2  how  many  times  ? 
75  contains  3  how  many  times  ? 
68  contains  2  how  many  times  ? 

6 1.  At  5  dimes  each,  how  many  turkeys  can  be  had 
for  25  dimes  ? 

62.  If  the  wages  of  1  day  is  4  climes,  what  will  be  the 
wages  for  9  days  ? 

63.  How  many  days  will  a  man  be  required  to  work 
"for  12  dimes,  if  he  receive  4  dimes  a  day? 


38  DIVISION. 

64.  If  a  boy  spends  5  cents  a  day,  how  many  days 
will  it  take  him  to  spend  15  cents  ? 

65.  A  boy  had  20  marbles,  and  divided  them  equally 
among  his  5  brothers ;  how  many  did  each  receive  ? 

66.  A  boy  divided  28  cents  equally  among  4  poor 
women  ;  how  many  cents  did  each  receive  ? 

67.  A  farmer  gave  4=  of  his  laborers  32  bushels  of 
corn ;  how  many  bushels  did  each  receive  ? 

68.  If  5  quarts 'of  ale  cost  30  cents,  what  will  1  cost  \ 

69.  At  5  cents  a  yard,  how  many  yards  of  ribbon 
may  be  had  for  35  cents  ?  how  many  for  50  cents  2 

70.  How  many  pine-apples,  at  8  cents  each,  can  be 
obtained  for  40  cents  ?   for  56  cents  ? 

71.  If  a  man  travel  45  miles  in  9  hours,  how  many 
miles  does  he  travel  in  1  hour  ? 

72.  If  a  man  travel  5  miles  in  an  hour,  how  many 
hours  will  it  take  him  to  travel  40  miles  ? 

73.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
can  you  buy  for  32  dollars  ? 

74.  In  a  certain  orchard   are  48  tree1;   standing  in 
rows,  and  6  trees  in  each  row ;  how  many  rows 
are  in  the  orchard  ? 

75.  For  56  dollars,  how  many  barrels  of  pork  can  be 
bought,  at  8  dollars  a  barrel  ? 

NOTE. — See  Methods  of  Teaching  and  Key  to  Intellec- 
tual Arithmetic,  page  28. 

76.  If  a  man  can  travel  6  miles  in  an  hour,  in  how 
many  hours  can  he  travel  42  miles  ? 

77.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
can  you  buy  for  36  dollars  ? 

78.  A  butcher  gave  39  dollars  for  sheep,  at  the  rate 
of  3  dollars  each ;  bow  many  sheep  did  he  buy  ? 

79.  45  dollars  were  given  for  9  barrels  of  flour ;  how 
much  was  it  a  barrel  ? 

80.  How  long  would  it  take  to  travel  72  miles,  at  the 
rate  of  3  miles  an  hour  ? 


DIVISION.  39 

LESSON     XI. 

1.  20  are  how  many  times  2  ?     4  ?     6  ? 

2.  22  are  how  many  times  11  ? 

3.  24  are  how  many  times  3  ?     4  ?     2  ? 

4.  25  are  how  many  times  5  ? 

5.  28  are  how  many  times  2  ?     7? 

6.  30  are  how  many  times  2  ?     3  ?     5  ? 

7.  32  are  how  many  times  2?     4?     16?     8? 

8.  34  are  how  many  times  17  ? 

9.  40  are  how  many  times  2  ?     4  ?     5  ?     8  ? 

10.  44  are  how  many  times  2  ?     11  ? 

11.  46  are  how  many  times  23? 

1 2.  48  are  how  many  times  2  ?     3  ?     4  ?     6  ? 

13.  50  are  how  many  times  2  ?     10  ? 

14.  56  are  how  many  times  2?     7? 

15.  57  are  how  many  times  3  ? 

1 6.  60  are  how  many  times  2?     3?     4?     5?     6? 

17.  64  are  how  many  times  2  ?     4  ?     8  ? 

1 8.  66  are  how  many  times  2?     3?     6? 

19.  68  are  how  many  times  2?     4? 

20.  70  are  how  many  times  10  ?     2  ? 

21.  72  are  how  many  times  2?     4?     6?     8? 

22.  5  are  how  many  times  2,   and  how  many  re- 
maining ? 

REMARK. — Whenever  there  is  a  remainder,  it  may  be 
mentioned  simply  as  a  remainder. 

23.  7  are  how  many  times  2  ? 

24.  17  are  how  many  times  4  ?  2  ?  5  ? 

25.  18  are  how  many  times  6  ?  4  ?  2  ? 

26.  34  are  how  many  times  4  ?  6  ?  5  ?     2  ? 

27.  25  are  how  many  times  5  ?  4  ?  2  ?     3  ? 

28.  16  are  how  many  times  9  ?  4  ?  8  ?     7  ? 

29.  32  are  how  many  times  7  ?  5  ?  6  ? 

30.  63  are  how  many  times  9?  4?  5?     6? 

31.  74  are  how  many  times  2  ?  4  ?  6  ?     7  ? 


40  DIVISION. 

32.  80  are  how  many  times  2?3?4?5?6?7?8? 

33.  84  are  bow  many  times  2 '?   3  ?  4  ?  5  ?  6  ?  7  ?  8 1 

34.  15  are  how  many  times  4  ?    6  ?  7  ?  8  ? 

35.  29  are  how  many  times  2?3?4?5?6?7? 

36.  90  are  how  many  times  2  ?   4  ?  6  ?  8  ?  9  ?  11 1 

37.  144  are  how  many  times  2  ?  4?  6?  8?  12? 


LESSON     XII. 

1.  At  2  cents  each,  how  many  lemons  can  I  buy  for 
14  cents  ? 

ANALYSIS  IST. —  If  1  lemon  cost  2  cents,  for  14  cents  I 
can  buy  as  many  lemons  as  2  is  contained  times  in  14, 
which  are  7  times. 

ANALYSIS  2x>. — If  for  2  cents  1  can  buy  1  lemon,  for  1 
cent  I  can  buy  1  half  of  a  lemon,  and  for  14  cents,  14 
times  1  half,  which  are  14  halves,  or  7  lemons. 

2.  How  many  boxes  of  cheese,  at  4  dollars  a  box., 
may  be  had  for  12  dollars  ? 

3.  If  one  hundred  pounds  of  hay  cost  3  dollars,  how 
many  hundred  may  be  had  for  15  dollars  ? 

4.  If  one  barrel  of  flour  support  20  persons  one  week, 
how  many  persons  will  it  support  4  weeks  ? 

5.  If  1  man  can  ride  1  mile  for  4  cents,  how  far  can 
2  men  ride  for  80  cents  ? 

6.  If  10  men  accomplish  a  certain  piece  of  work  in  2 
days,  how  long  will  it  take  1  man  to  do  the  same  > 

7.  If  3  yards  of  cloth  make  1  coat,  how  many  coats 
will  18  yards  make  ? 

8.  If  I  receive  12  dollars  interest  in  one  year,  in  how 
many  years  will  I  receive  144  dollars  interest  ? 

9.  A  man  traveled  7  miles  in  1  hour,  at  the  same 
rate  how  long  would  it  take  him  to  travel  63  miles  ? 

10.  If  1  cow  cost  13  dollars,  how  many  cows  may  be 

had  for  65  dollars  ? 
u.  How  many  pens  can  you  buy  for  27  cents,  if  1 

pen  cost  3  cents  ? 


DIVISION.  41 

12.  If  8  apples  are  worth  40  chestnuts,  how  many 
chestnuts  is  1  apple  worth  ? 

13.  How  many  cents  is  1  lemon  worth,  if  12  lemons 
are  worth  48  cents  ? 

14.  How  much  will  1  cord  of  wood  cost,  if  20  cords 
cost  40  dollars  ? 

15.  If  1  pound  of  beef  cost  7  cents,  how  much  will 
19  pounds  cost  ? 

1 6.  For  147  cents,  how  many  pounds  of  sugar  can  be 
bought,  at  7  cents  a  pound  \ 

17.  If  9  yards  of  cloth  cost  53  dollars,  for  how  much 
must  it  be  sold  a  yard  to  gain  10  dollars  ? 

1 8.  If  7  barrels  of  flour  cost  38  dollars,  and  were  sold 
at  7  dollars  a  barrel,  what  was  the  gain  \ 

19.  How  many  peaches,  at   4  cents   each,  may   be 
bought  for  96  cents  ? 

20.  How  many  yards  of  cloth,  at  4  dollars  a  yard 
can  be  bought  for  116  dollars  ? 

21.  How  many  oranges,  at  3  cents  each,  must   bf* 
given  for  18  lemons  worth  4  cents  each  ? 

22.  If  15  sheep  cost  75  dollars,  what  will  1  sheep  cost . 

23.  Will  4  barrels  of  wheat  flour  at  9  dollars  a  bar- 
rel, cost  more  than  12  barrels  of  corn  at  4  dollar^ 
a  barrel  ?   how  much  more  ? 

24.  How  many  barrels  of  beef,  at  3  dollars  a  barrel, 
can  be  bought  for  54  dollars  ? 

25.  How  many  pounds  of  fish,  at  5  cents  a  pound, 
may  be  had  for  95  cents  ? 

26.  At  7  cents  a  pound,  how  many  pounds  of  lead 
may  be  had  for  84  cents  ? 

27.  How  long  v/ill  it  require  to  travel  105  miles,  at 
the  rate  of  5  miles  an  hour  ? 

28.  A  person  divided  72  peaches  equally  among  6 
boys ;  how  many  did  each  receive  ? 

29.  148  marbles  were  divided  equally  among  some 
boys ;  how  many  boys  were  therej  provided  each 
bov  received  2  marbles  ? 


4i$  DIVISION. 

30.  How  many  pounds  of  butter,  at  14  cents  a  pound, 
can  be  bought  for  28  apples,  at  3  cents  each  ? 

31.  At  7  cents  a  bottle,  how  many  bottles  of  ink  can 
you  buy  for  14  sheets  of  paper,  at  2  cents  a  sheet  ? 

32.  In  how  many  days  can  1  man  do  as  much  as  7 
men  in  8  days  ? 

33.  In  how  many  days  can  2  men  do  as  much  work 
as  6  men  in  3  days  ? 

ANALYSIS. — If  6  men  can  do  a  certain  amount  of  work 
in  3  days,  1  man  can  do  the  same  work  in  '6  times  3  days, 
which  are  18  days  ;  and  2  men  can  do  it  in  one-half  of  18 
days,  which  is  9  days. 

34.  In  how  many  days  can  4  men  earn  as  much  as  8 
men  in  6  days  ? 

35.  In  how  many  days  can  15  men  earn  as  much  as 
3  men  in  25  days  ? 

36.  In  how  many  months  will  6  horses  eat  as  much 
as  18  horses  in  5  months  ? 

37.  How  many  men  can  in  7  days  earn  as  much  as 
28  men  in  4  days  ? 

38.  In  10  days  6  men  will  earn  as  much  as  how  many 
men  in  5  days  ? 

39.  How  many  yards  of  cloth,  v\  4  dollars  a  yard, 
may  be  had  for  4  sets  of  ch.irs,  at  12  dollars  a 
set  ? 

40.  A  farmer  gave  13  barrels  of  flour,  worth  4  dollars 
a  barrel,  for  20  yards  of  cloth ;   how  much  was 
the  cloth  a  yard  ? 

41.  The  dividend  is  108,  and  the  divisor  is  12;  re- 
quired the  quotient. 

42.  The  dividend  is  96,  and  the  quotient  is  4 ;  what 
is  the  divisor  ? 

43.  The  quotient  is  7,  and  the  divisor  is  9 ;  what  is 
the  dividend  I 


FUNDAMENTAL     K  U  L  E  S  .  43 

LESSON     XIII. 

THE  FOUB  FUNDAMENTAL  RULES  COMBINED. 

1.  4  times  6  are  how  many  times  2  ? 

ANALYSIS— 4  times  6  are  24.    24  are  12  times  2.    There- 
fore,  4  times  G  are  12  times  2. 

2.  4  times  9  are  ho\v  many  times  3  ? 

3.  4  times  8  are  how  many  times  2  ? 

4.  4  times  10  are  how  many  times  5  ? 

5.  4  times  12  are  how  many  times  6  ? 

6.  4  times  14  are  how  many  times  7  ? 

7.  5  times  9  are  how  many  times  15  ? 

8.  5  times  8  are  how  many  times  4  ? 

9.  5  times  12  are  how  many  times  15  ?     6  ? 

10.  6  times  7  are  how  many  times  2  ? 

1 1.  0  times  8  are. how  many  times  12  ?     3  ? 

12.  4  times  6  are  how  many  times  8  ? 

13.  7  times  15  are  how  many  times  5  ? 

14.  12  times  7  are  how  many  times  21  ? 

15.  8  times  7  are  how  many  times  4  ?  > 

1 6.  How  many  times  12  are  9  times  4  ? 

17.  How  many  times  20  are  5  times  4  ? 

1 8.'  How  many  times  9  are  3  times  21,  +9  ? 

19.  How  many  times  5  are  7  times  15,  +10—5  ? 

20.  How  many  times  9  are  3  times  36,  —2  +  11  ? 

21.  How  many  times  12  are  9  times  4,  +24—12  ? 

22.  How  many  times  21  are  9  times  14,  +42  ? 

23.  How  many  times  7  are  3  times  14,  +21  —  14? 

24.  How  many  times  5  are  8  times  10,  +5—15  ? 

25.  How  many  times  5  are  10  times  6,  +15  +  5  ?. 

26.  How  many  times  5  are  6  times  15,  +10  +  15  ? 

27.  10  times  4,  +2,  are  how  many  times  7  ?     2  ? 

28.  8  times  9,  — 2,  are  how  many  times  5  ? 

29.  12  times  8,— 8,  are  how  many  times  2  ? 

30.  26  times  11,— 6,  are  how  many  times  28  ? 

31.  7  times  8,  +  4,  are  how  many  times  12  ? 


44  SIMPLE     PROPORTION. 

LESSON     XI V. 

QTF5STIONS  COMBINING  MULTIPLICATION  AND  DIVISION. 

*i.  If  2  apples  cost  4  cents,  how  many  cents  will  3 
apples  cost  ? 

ANALYSIS. — If  2  apples  cost  4  cents,  1  apple  will  cost  1 
half  of  4  cents,  which  is  2  cents.  If  1  apple  costs  2  cents, 
8  apples  will  cost  o  times  2  cents,  which  are  6  cents. 

2.  If  2  pears  cost  16  cts.,  how  much  will  5  pears  cost  ? 

3.  If  4  quinces   cost  12  cents,   how  much  will  3 
quinces  cost  ? 

4.  If  6  oranges   cost  18  cents,  how  much  wrill  9 
oranges  cost  ? 

5.  If  7  peaches   cost  21  cents,  how  much  will  9 
peaches  cost  ? 

6.  If  4  lemons   cost   24  cents,   how  much  will  7 
lemons  cost  ? 

7.  If  3  yards  of  tape  cost  18  cents,  how  much  will  6 
yards  cost  ? 

8.  If  7  hair-brushes  cost  28  dimes,  how  many  cents 
will  6  hair-brushes  cost  ? 

9.  If  9  yards  of  muslin  cost  108  cents,  how  much 
will  7  yards  cost  ? 

10.  If  11  books  cost  44  dimes,  how  many  cents  will 
7  books  cost  ? 

11.  If  12  ink-stands  cost  96  cents,  what  will  2  cost  ? 

12.  If  10  lead-pencils  cost  30  cents,  how  much  will 
be  the  cost  of  7  ?  of  9  ?  of  2  ?  of  15  ?  of  12  ? 

13.  How  much  will  13  yards  of  silk  cost,  if  5  yards 
cost  45  dimes  ? 

14.  If  a  man  travel  1 5  miles  in  3  hours,  how  far,  at  this 
rate,  can  he  travel  in  9  hours  ?  5  hours  ?  7  hours  ? 

15.  If  the  cartage  of  a  load  of  plaster  20  miles  cost  4 
dollars,  how  far  could  it  be  carried  for  12  dollars  ? 

1 6.  How  many  pairs  of  pantaloons  can  be  cut  out  of 
21  yards  of  cloth,  if  3  pairs  can  be  cut  out  of  9 
yards  of  the  same  kind  of  cloth  ? 


SIMPLE     PROPORTION.  45 

17.  How  much  will  30  pounds  of  sugar  cost,  if  6 
pounds  cost  42  cents  ? 

1 8.  How  much  will  18  pounds  of  veal   cost,  if  6 
pounds  cost  42  cents  ? 

19.  How  much  will  75  pounds  of  pork  cost,  if  9 
pounds  cost  75  cents '( 

20.  How  much  will  20  weeks'  board  amount  to,  if  7 
weeks'  board  cost  35  dollars  ? 

21.  How  much  will  be  the  wages  for  one  year,  if  4 
months'  wages  amount  to  48  dollars  ? 

22.  How  much  will  be  the  cost  of  25   bushels  of 
apples,  if  13  bushels  cost  260  cents  ? 

23.  How  much  will  14  pounds  of  cheese  cost,  if  6 
pounds  cost  54  cents  \ 

24.  What  cost  36  quarts  of  milk,  at  35  cts.  for  7  qt.  ? 

25.  If  4  men  can  do  a  piece  of  work  in  12  days,  in  how 
many  days  can  3  men  do  the  ^ame  work  ? 

26.  I  gave  72  dollars  for  a  quantity  of  cotton,  and 
sold  it  for  12  yards  of  cloth ;  how  much  did  the 
cloth  cost  me  a  yard  ? 

27.  Gave  15  pounds  of  sugar  for  5  pounds  of  butter; 
how  much  did  the  butter  cost  a  pound,  provided 
8  pounds  of  sugar  wTere  worth  56  cents  ? 

28.  If  4  chestnuts  are  worth  8  walnuts,  how  many 
walnuts  are  27  chestnuts  worth  ? 

29.  If  7  yards  of  broadcloth  are  worth  35  dollars, 
how  many  boxes  of  butter,  at  3  dollars  a  box, 
would  9  yards  of  this  cloth  buy  ? 

30.  A  man  bought  4  barrels  of  flour  for  20  dollars, 
and  gave  3  of  them  for  cider,  at  3  dollars  a  bar- 
rel ;  how  many  barrels  of  cider  did  he  get  ? 

31.  A  man  bought  14  barrels  of  cider  for  56  dollars, 
and  gave  5  barrels  of  it  for  cloth,  at  2  dollars  a 
yard ;  how  many  yards  did  he  receive  ? 

32.  A  merchant  having  15  yards  of  cloth  worth  75 
dollars,  gave  10  of  them  for  pork,  worth  10  dol- 
lars a  barrel;  how  many  barrels  did  he  receive  ? 


4:0  SIMPLE     P  K  O  P  O  li  TI  O  N  . 

33.  When  9  bushels  of  rye  were  worth  45  dimes,  12 
bushels  were  given  for  15  yards  of  cloth;   how 
much  did  the  cloth  cost  a  yard  ? 

34.  If  35  yards  of  cloth  cost  140  dollars,  how  much 
will  95  yards  of  the  same  cloth  cost  '4 

35.  Two  boys  are  32  rods  apart,  and  both  running  in 
the  same  direction,  the  hindermost  boy  gains  on 
the  other  4  rods  each  minute ;  in  how  many  min- 
utes will  he  overtake  him  ? 

36.  How  many  boxes  will  be  required  to  contain  56 
bushels,  provided  each  box  contains  8  bushels  ? 

37.  How  many  barrels  of  onions,  at  3  dollars  a  bar- 
rel, must  be  given  for  21  boxes  of  raisins,  at  2 
dollars  a  box  ? 

38.  A  farmer  bought  9  yards  of  cloth,  at  4  dollars  a 
yard,  and  paid  for  it  with  cider,  at  3  dollars  a 
barrel ;  how  many  barrels  did  it  take  ? 

39.  How  long  would  it  take  a  man  t©  save  24  dollars, 
if  he  save  2  dollars  a  week  ? 

40.  A  farmer  hired  a  laborer  and  agreed  to  give  him 
6  dollars  for  every  3  days'  work ;  how  much  did 
he  receive  a  week,  allowing  6  working  days  in  a 
week  ?    how  much  a  month,  allowing  4  weeks  to 
the  month  ? 

41.  If  4   oranges    are    worth    12  cents,   how  many 
oranges  must  be  given  for  6  pine-apples,  worth 
12  cents  each  ? 

42.  How  many  yards  of  cloth,  at  $2  a  yard,  can  be 
bought  for  4  reams  of  paper,  at  5  dollars  a  ream  ? 

43.  It'  2  apples  are  worth  .1  orange,  and  2  oranges 
are  worth  1  lemon  ;   how  many  lemons  can  be 
bought  for  48  apples  \ 

44.  If  7  men  can  do  a  certain  job  of  work  in  12  days, 
in  how  many  days  could  21  men  do  the  same  work  ? 

45.  Bought    5  firkins  of  butter  for  35  dollars ;    for 
what  must  I  sell  it  to  gain  10  dollars ;  what  is 
the  gain  on  each  firkin  ? 


TABLES,    AND     REDUCTION.  47 

LESSON     XV. 

COMPOUND    DENOMINATE    NUMBERS. 

TABLE  OF  UNITED   STATES  CURRENCY. 

10  Mills  (w.)  make  1  Cent,  marked    ct. 

10  Cents                  "  1  Dime,  d. 

10  Dimes                  "  1  Dollar,  "           $. 

10  Dollars                "  1  Eagle,  E. 

1.  How  many  mills  in  4  cents  'I 

ANALYSIS. — In  1  cent  there  are  10  mills,  and  in  4  cents 
there  are  4  times  10  mills,  or  40  mills. 

2.  How  many  mills  in  3  cents  ?    In  5  cents  ?    In  8  ? 

3.  How  many  cents  in  2  dimes  ?     In  4  dimes  ?     In 
5  dimes  (\  In  6  dimes  ?  In  9  dimes  ?  In  10  dimes  '* 

4.  How  many  dimes  in  $1  ?     In  $2  ?     In  $3  ?     In 
$4*     In  $5?     In  ,$6? 

5.  How  many  dimes  in  1  E.  and  $4  ?    In  2  E.  and  $8  ? 

6.  How  many  cents  in  $1  ?    In  $2  ?   In  $3  ?   In  $4  2 

7.  How  many  dollars  in  80  dimes  ? 

ANALYSIS. — There  are  10  dimes  in  $1;  therefore.  1  tenth 
of  the  number  of  dimes  equals  the  number  of  dollars. 
1  tenth  of  80  is  8.  Therefore,  in  80  dimes  there  are  $8. 

8.  How  many  dimes  in  60  cents  ?     In  70  cents  ? 

9.  How  many  dollars  in  200  cents  1     In  500  cents  2 
In  800  cents  ?     In  360  cents  ?     In  705  cents  ? 

10.  If  3  yards  of  muslin  cost  6  dimes,  how  many 
yards  can  be  bought  for  $1  \ 


LESSON     XYI. 

TABLE    OF    ENGLISH    MONEY. 

4  Farthings  (far.)    make  1  Penny,    marked  d. 

12  Pence  "      1  Shilling,       "        #. 

20  Shillings  "      1  Pound,          "        £. 

A  Sovereign  (sov.)  is  equal  in  value  to  £lk 


48  TABLES     AtfD     REDUCTION. 

1.  How  many  shillings  in  £4  15  shillings  ? 

ANALYSIS  IST.— There  are  20  shillings  in  £1  ;  therefore, 
20  times  the  number  of  pounds  equal  the  number  of  shil- 
lings. 20  times  4  are  80  shillings,  + 15,  are  95  shillings. 

ANALYSIS  2D. —  In  £1  there  are  20  shillings,  and  in  £4 
there  are  4  times  20  shillings,  which  are  80  shillings.  80 
shillings  +15  shillings,  are  95  shillings. 

2.  How  many  pence  in  1  shilling  ?     In  4  shillings  ? 
In  3  shillings  ?     In  7  shillings  ?     In  9  shillings  ? 

3.  How  many  shillings  in  £1  ?     In  £2  ?     In  £3  ? 

4.  How  many  pence  in  £2  10  shillings  5  pence  ? 

5.  Hosvr  many  pounds  in  60  shillings  '2     In  86s.  ? 

6.  How  many  pounds  in  480  pence  ?     In  720rf.  ? 

7.  At  4  shillings  a  bushel,  how  many  pounds  will 
40  bushels  of  potatoes  cost  ? 

8.  At  10  pence  each,  how  many  pounds  will  48  pine- 
apples cost  ? 

9.  At  5  shillings  a  yard,  how  many  yards  of  cloth 
can  be  bought  for  £2  15  shillings  ? 


LESSON     XVII. 

TABLE   OF   TROY  WEIGHT. 

24  Grains  (gr.)     make  1  Pennyweight,    marked  pwt. 
20  Pennyweights     "       1  Ounce,  oz. 

12  Ounces  1  Pound,  ». 

1.  How  many  pennyweights  in  240  grains  ? 

2.  How  many  pennyweights   in   4   ounces  {(     In   5 
ounces  ?     In  6  ounces  ? 

'.3.  How  many  ounces  in  1  pound?     In  3  pounds? 
In  5  pounds  ?     In  8  pounds  ? 

4.  In  24  ounces  how  many  pounds  ?     In  48  ounces  ? 
In  36  ounces  ?     In  60  ounces  ?     In  84  ounces  ? 

5.  How  many  ounces  in  20  pennyweights  ?     In  40  ? 
In  60  ?     In  70  ? 


TABLES     AND     KEDCCTION.  4:9 

>.  If  7  grains  of  gold  cost  2  dimes  and  8  cents,  how 

much  will  10  pennyweights  cost  ? 
r.  How  many  pounds  in  480  pennyweights  ? 
!.  How  many  grains  in  2  oz.,  2  pwt.,  and  2  gr.  ? 


LESSON    XVIII. 

TABLE   OF   AVOIRDUPOIS   WEIGHT. 

16  Drams  (dr.)  make  1  Ounce,               marked  oz. 

16  Ounces  "      1  Pound,                    "        Ib. 

25  Pounds  "       1  Quarter,                  u        qr. 

4  Quarters,  or  100  Ib.  "      1  Hundred-weight,   "        cwl. 

20  Hundred-weight  "      1  Ton,                                 T. 

1.  How  many  drams  in  2  oz.  ?    In  4  oz.  ?    In  10  oz.  ? 

2.  How  many  ounces  in  2  Ib.  ?     In  4  Ib.  ?     In  8  Ib.  ? 

3.  How  many   quarters   in    100   pounds  ?      In   400 
pounds  ?     In  600  pounds  ?     In  1200  pounds  ? 

4.  How  many  pounds  in  3  qr.  ?    In  2  qr.  ?    In  7  qr.  ? 

5.  How  many  quarters  in  2  hundred- weight  ? 

6.  In  8  quarters  how  many  hundred-weight  ? 

7.  What  will  2  tons  of  iron  cost,  if  1  Ib.  cost  1  dime  ? 

8.  What  will  40  tons  of  hay  cost,  at  2  dimes  a  qr.  ? 


LESSON      XIX. 

TABLE    OF    LONG   MEASURE. 


12 
3 

40 
8 
3 

360 

Inches  (in.)               mi 
Feet 
Yards,  or  16i  feet, 
Rods 
Furlongs,  or  320  rods, 
Miles 
Miles 
Degrees 
3 

ike  1  Foot,            marked  ft. 
1  Yard,                 «        yd. 
1  Rod,                  "        rd. 
1  Furlong,           "       fur. 
1  Mile,                           mi. 
1  League,             "        lea. 
1  Degree,             "        <%.,ora 
1  Circle  of  the  earth. 

50  TABLES     AND     REDUCTION. 

j.  How  many  inches  in  1  ft.  ?     In  2  ft.  ?     In  4  ft.  ? 
In  5  ft.  ?     In  10  ft.  ? 

2.  How  many  feet  in  2  yd.  ?     In  6  yd.  ?     In  5  yd.  ? 

3.  How  many  yards  in  2  rods  ?    In  4  rd.  ?    In  8  rd.  ? 

4.  How  many  furlongs  in  4  miles  ?     In  6  mi.  ? 

5.  How  many  inches  in  4  yd.  2  ft.  10  in.  ? 

6.  In  216  inches,  how  many  yards  ?     In  288  in.  ? 

7.  How  many  rods  in  1  mile  ? 

8.  How  many  miles  in  1760  yards  ? 

9.  How  many  feet  in  2  rods  5  yd.  2  ft.  11  in.  ? 

10.  How  many  feet  in  1  mile  ? 

LESSOJST     XX. 

TABLE    OF    CLOTH    MEASURE. 

In  Cloth  Measure,  the  Yard  is  the  unit  of  measure,  and  is 
divided  into  Halves,  Fourths,  Eighths,  and  Sixteenths.  The  fol- 
lowing Table  was  formerly  used  : 

2£  Inches        make  1  Nail,  marked  na. 


4  Nails 

4  Quarters 
3  Quarters 

5  Quarters 

6  Quarters 


1  Quarter  of  a  yard,  "  qr. 

1  Yard,  "  yd. 

1  Ell  Flemish,  "  E.  VI. 

1  Ell  English,  k'  E.  E. 

1  Ell  French,  "  E.  Fr. 


o    quarters  i  juii  Jb  rencn, 

1.  In  4  yd.  3  qr.,  how  many  quarters  ? 

2.  In  7  yd.  2  qr.,.  how  many  Ells  French  \ 

3.  In  3  yd.  3  qr.,  how  many  Ells  Flemish 


LESSON     XXI. 

TABLE    OF    LAND   MEASURE. 


144    Square  inches  (sq.  in.) 
9    Square  feet 
30£  Square  yards 
40    Square  rods 
4    Roods 
640    Acres 

make  1  Square  foot,              sq.ft. 
"      1  Square  yard,             817.  yd 
u      1  Square  rod,  or  pole,  P. 
"       1  Rood,                         It. 
"       1  Acre,                         A. 
"       1  Square  mile,              sq.  in. 

TABLES     AND     REDUCTION 


51 


1.  How  many  square  feet  in  4  sq.  yd.  ?    In  8  sq.  yd.  ? 

2.  How  many  poles  in  4  roods  ?     In  6  roods  ? 

3.  How  many  acres  in  40  roods  ?     In  160  roods  ? 

4.  How  many  square  yards  in  81  sq.  ft.  3  In  108  sq.  ft.  ? 

5.  How  many  square  yards  in  1  rood  10  rods  ? 


LESSON     XXII. 


TABLE    OF    CUBIC    MEASURE. 


1728    Cubic  inches  (cu.  in.) 
27    Cubic  feet 
24f  Cubic  feet 
16    Cubic  feet 
8    Cord  feet,  or 
128    Cubic  feet 


make  1  Cubic  foot,  cu.ft. 

"  1  Cubic  yard,  cu.  yd. 

"  1  Perch  of  stone,  pch. 

"  1  Cord  foot,  c.ft. 

"  1  Cord  of  wood,  C. 


1.  How  many  cubic  feet  in  4  cubic  yards  ? 

2.  How  many  cubic  feet  in  4  perch  of  stone  ? 

3.  How  many  cords  in  96  cord  feet  ?     In  72  c.  ft.  ? 

4.  How  many  cords  in  128  cu.  ft.  ?     In  384  cu.  ft.  ? 

5.  How  many  cord  feet  in  4  cords  ?     In  6  cords  ? 


LESSON     XXIII. 

TABLE    OF    WINE    MEASURE. 

z'.)                    im 

ike  1  Pint,           mai 
1  Quart 
1  Gallon, 
1  Tierce, 
1  Barrel, 

•ked  pt. 

qt 
gal. 
tier, 
bar. 

or  63  Gallons,          1  Hogshead, 
ids                     "      1  Pipe, 
"      1  Tun, 

lihd. 
pi. 
tun. 

4  Gills  (gi.) 

2  Pints 

4  Quarts 

42  Gallons 
31 1-  Gallons 

2  Barrels, 

2  Hogshe; 

2  Pipes 

NOTE. — Barrels,  tierces,  hogsheads,  pipes,  and  tuns  are  not 
measures,  but  vessels  of  variable  capacity,  which  are  gauged, 
the  contents  being  sold  by  the  gallon. 


52  TABLES     AND     REDUCTION. 

1 .  How  many  gills  in  3  pints  ?     In  4  pints  ? 

2.  In  3  qt.,  how  many  gills  ? 

3.  In  12  gallons,  how  many  pints  ? 

4.  What  will  5  gall,  of  rum  cost,  if  4  gi.  cost  5  cents? 

5.  How  many  pints  in  2  pipes  ? 

6.  A  merchant  bought  a  hogshead  of  molasses  for  20 
dollars,  and  sold  it  at  the  rate  of  15  cents  for  3 
pints ;  how  much  did  he  gain  by  the  bargain  ? 

7.  What  will  1  gall,  of  wine  cost,  at  21  cents  for  7  gi.? 

8.  In  4  quarts  and  2  pints,  how  many  gills  ? 


LESSON     XXI Y. 

TABLE    OP    DRY    MEASURE. 

2  Pints        make  1  Quart,     marked  qt. 
8  Quarts        "       1  Peck,  "        pic. 

4  Pecks         "      1  Bushel,        ",      bu. 

1.  In  1  peck,  how  many  pints  ? 

2.  2  pecks  will  fill  how  many  pint  measures  ? 

3.  In  3  pecks  and  3  quarts,  how  many  pints  ? 

4.  In  1  bushel  and  3  pecks,  how  many  quarts  ? 

5.  In  1  bushel,  how  many  quarts  ?   how  many  pints  ? 

6.  If  8  pints  of  nuts  cost  24  cents,  what  will  3  pecks 
cost  at  the  same  rate  ? 

7.  A  market  woman  bought  4  quarts  of  strawberries 
for  29  cents,  and  sold  them  at  5  cents  a  pint ;  how 
much  did  she  gain  ? 

8.  A  person  sold  2  bushels  and  1  peck  (or  144  pints) 
of  currants,  at  2  cents  a  pint,  and  in  payment  re- 
ceived 1  bushel  (or  64  pints)  of  gooseberries,  at  4 
cents  a  pint ;  how  much  remains  due  ? 

9.  What  will  5  quarts  of  wheat  cost,  if  1  bushel  cost 
128  cents  ? 


TABLES     AND     REDUCTION 


LESSON     XX  Y. 


TABLE    OF    TIME. 


60  Seconds  (sec.)         make  1  Minute,           marked  m. 

60  Minutes 

1  Hour, 

lir. 

24  Hours 

1  Dav, 

d. 

7  Days 

1  Week, 

w. 

4  Weeks 

1  Month, 

mo. 

12  Calendar  Months 

1  Year, 

yr. 

52  Weeks 

1  Year, 

yr. 

365  Days 

1  Common  Year, 

yr. 

366  Days 

1  Leap  Year, 

yr. 

100  Years 

1  Century, 

a. 

The  following  Table  exhibits  the  divisions  of  the 
year,  the  names  of  the  months,  and  the  number  of 
in  each  : — 


I 


1st 

month, 

January, 

has 

31 

days. 

2d 

month, 

February, 

has 

28, 

in  leap  year  29. 

3d 

month, 

March, 

has 

31 

days. 

4th 

month, 

April, 

has 

30 

days. 

5th 

mouth, 

May, 

has 

31 

days. 

6th 

month, 

June, 

has 

30 

days. 

7th 

month, 

July, 

has 

31 

days. 

8th 

month, 

August, 

has 

31 

days. 

9th 

month, 

September, 

has 

30 

days. 

10th 

month, 

October, 

has 

31 

clays. 

llth 

month, 

November, 

has 

30 

clays.' 

3?  j  12th  month,    December,    has     31  days. 

The   following   lines  will   help  to  remember  the 
number  of  days  in  each  month  : 

"  Thirty  days  hath  September, 
April,  June,  and  November; 
All  the  rest  have  thirty-one, 
Except  February  alone, 
Which  hath  but  twenty-eight  in  fine, 
Till  leap  year  gives  it  twenty-nine." 


54  TABLES     AND     REDUCTION. 


In  OUT  calculations  on  interest  we  shall  reckon  30  days  to 
the  month,  and  12  months  to  the  year,  although  not  strictly  'accu- 
rate. [See  New  Practical  Arithmetic,  page  184.] 

1.  In  2  hours,  how  many  seconds  ? 

2.  In  2  weeks  and  5  days,  how  many  days  1 

3.  In  48  hours,  how  many  days  ? 

4.  In  7200  seconds,  how  many  hours  ? 

5.  How  many  hours  in  a  week  ? 

6.  In  1  day  12  hours  and  10  minutes,  how  many 
minutes  ? 

7.  How  many  hours  in  a  month  ? 

8.  If  a  boy  can  do  a  certain  piece  of  work  in  40  min- 
utes, how  many  hours  would  it  take  him  to  per- 
form 12  times  as  much  work  ? 

9.  If  I  can  do  a  piece  of  work  in  10  minutes,  how 
many  hours  would  it  take  to  perform  12  times  as 
much  work  ? 

10.  How  many  days  in  3  weeks  and  5  days  ? 


LESSON     XXYI. 

MISCELLANEOUS    TABLE. 

12  Units  make     1  Dozen. 


13  Dozen 
12  Gross 
•20  Units 

24  Shee is  of  Paper 
20  Quires 
56  Pounds 
60  Pounds 
196  Pounds 


1  Gross. 

1  Great  Gross. 

1  Score. 

1  Quire. 

1  Ream. 

1  Bushel  of  Corn  or  Rye. 

1  Bushel  of  Wheat. 

1  Barrel  of  Flour. 


onn  n        i  i  1  Barrel  of  Beef, 

200  Pounds  |      Pork,  or  Fish. 

1 .  "What  will  2  reams  of  paper  cost,  at  15  cents  a  quire  ? 

2.  How  many  sheets  of  paper  in  1  ream  ? 

3.  How  many  years  in  "3  score  years  'and  10  "? 

4.  How  many  units  in  a  gross  ? 


TABLES     AND     REDUCTION.  55 

LESSON     XXYI. 

METRICAL  WEIGHTS  AND   MEASURES. 

In  France  and  several  other  countries  of  Europe,  the  division 
of  Weights  and  Measures  is  on  the  decimal  system.  On  this 
system  the  United  States  currency  is  founded,  and  its  applica- 
tion to  Weights  and  Measures  is  now  permitted  by  Congress. 

The  METRE  is  the  unit  in  measuring  lengths,  and  is  the 
basis  of  the  system.  It  is  one  ten-millionth  part  of  a  quadrant 
of  the  earth's  meridian,  or  that  part  of  the  earth's  circumfer- 
ence between  the  Equator  and  the  Pole.  The  Metre  is  nearly 
equal  to  3  feet  and  3£  inches.  5  Metres  =  1  Rod  nearly. 

The  ARE  is  the  unit  for  superficial  measure.  It  equals  the 
area  of  a  square  whose  side  is  ten  metres. 

The  STERE  is  the  unit  for  wood  and  cubic  measure.  It  is 
a  cubic  metre,  and  contains  100  litres. 

The  LITRE  is  the  unit  in  measures  of  capacity,  and  is  a  cubic 
decimetre.  The  litre  is  equal  to  a  little  more  than  a  quart 
wine  measure. 

The  GRAM  is  the  unit  of  weight,  and  is  the  weight  of  a 
cube  of  pure  water  at  the  temperature  of  melting  ice,  each 
edge  of  the  cube  being  Tf  ffth  of  a  metre.  The  gram  is  -equal 
to  very  nearly  15£  grains  Troy  weight. 

REMARK. — Each  of  these  units  is  divided  decimally,  and 
larger  units  are  formed  by  multiples  of  10,  100,  etc.  The  suc- 
cessive multiples  are  designated  by  the  prefixes  deka,  hecto, 
kilo,  myria  ;  the  parts  by  deci,  centi,  and  milli,  as  shown  by  the 
following  Tables. 

The  FRANC  is  the  unit  of  value,  and  is  a  coin  weighing  five 
grains.  It  is  equal  to  18  cents  6  mills  U.  S.  coin.  The  Dollar 
is  the  unit  of  value  in  U.  S.  currency. 

Note.— For  the  Numeration  and  Notation  of  Integers  and 
Decimals,  see  pages  171,  172. 

MEASURES    OF    LENGTH. 


10 

Millimetres     make     1 

Centimetre 

= 

.393685 

of  an  Inch. 

10 

Centimetres        ' 

1 

Decimetre 

— 

3.93685 

Inches. 

10 

Decimetres         * 

1 

METRE 

— 

39.3685 

U 

10 

Metres                ' 

1 

Dekametre 

= 

393.685 

U 

10 

Dekametres       ' 

1 

Hectometre 

= 

3936.85 

U 

10 

Hectometres      ' 

1 

Kilometre 

— 

39368.5 

U 

10 

Kilometres         "         1 

Myriametre 

= 

393685 

U 

56 


TABLES     AND     REDUCTION. 


I-  How  many  decimetres   are   in  1  metre?     In  3 
metres  ?     In  8  metres  ?     In  1  dekametre  ? 

2.  How  many  centimetres  are  in  1  metre  ? 

3.  How  many  millimetres  are  in  1  metre  ?     In   1 
decimetre  ?     In  1  dekametre  ?     In  1  hectometre  '( 
In  1  kilometre  ?     In  1  myriametre  ? 

4.  Then  how  many  metres  are  in  one  myriametre  ? 

5    One  metre  is  equal  to  how  many  inches  of  Long 
Measure  ?     A  myriametre  to  how  many  inches  ? 

MEASURES    OP    WEIGHT. 


DENOMINATION. 

DECIMAL                      COMPARATIVE 
EXPRESSION.                        WEIGHT. 

10  Milligram 

.001          =        .015434  of  a  Grain  (Troy  weight). 

make  1 

10  Centigram 

.01           =         .15434        "            " 

make  1 

10  Decigram 

.1              =          1.5434  Grains  (Troy  weight). 

make  1 

10  GRAM 

1            =         15.434      "            " 

make  1 

10  Dekagram 

10                     154.34      "            " 

make  1 

10  Hectogram 

100         =         1543.4      "            " 

make  1 

10  Kilogram 

1000       =         15434       "            " 

MEASURES    OF    CAPACITY,    ETC. 

10  Millilitres 

make     1  Centilitre      =     .61028  of  a  Cubic  Inch. 

10  Centilitres 

1  Decilitre       =     6.1028  Cubic  inches. 

10  Decilitres 

1  LITRE            =     61.028     "        " 

10  Litres 

"        1  Dekalitre      =     610.28     "        " 

10  Dekalitres 

"        1  Hectolitre     =     6102.8     «        " 

10  Hectolitres 

1  Kilolitre        =     61028.     " 

100  Centiares 

make    1  ARE.  1  100  Ares     make    1  Hectare,, 

10  Centisteres  make  1  Dec-istere.  |  10  Decisteres  make  1  STERE. 
10  Steres  make  1  Dekastere. 

FRENCH  CURRENCY. 

10  Millimes         make     1  Centime  =         .001  of  a  dollar. 

10  Centimes  "         1  Decime  =         .018        " 

10  Decimef  "         1  Franc  =         .186         " 

5  Franc  piece,  (silver)  =         .930        u 

20  Franc  piece,  or  Napoleon  (gold)  =  3.72    dollars. 


FRACTIONS.  57 

FRACTIONS. 

LESSON     XXVII. 

1.  John  has  6  nuts,  and  Joel  1  half  as  many;   how 
many  has  Joel  ? 

ANALYSIS. — If  John  has  6  nuts,  and  Joel  1  half  as  many, 
Joel  must  have  1  half  of  6  nuts,  which  is  3  nuts. 

2.  Mary  had  4  dresses,  and  Rachel  1  half  as  many ; 
how  many  had  Rachel  ? 

3.  Jacob  is  8  years  old,  and  John  is  1  half  as  old ; 
how  old  is  John  ? 

4.  Moses  had  2  marbles,  and  gave  1  half  of  them  to 
his  brother ;  how  many  had  he  left  ? 

5.  If  you  divide  6  apples  equally  between  2  boys, 
what  part  of  them  will  each  have  ? 

6.  What  is  1  half  of  6  ? 

7.  How  many  halves  in  1  ? 

8.  If  an  orange  cost  8  cents,  and  a  peach  1  half  as 
much ;  what  was  the  cost  of  the  peach  ? 

9.  James  had  12  cakes,  and  John  1  half  as  many; 
how  many  had  John  ? 

10.  If  3  apples  cost  6  cents,  what  part  of  6  cents  will 
1  apple  cost  ?     2  apples  ?     3  apples  ? 

11.  What  is  1  third  of  6  ?     2  thirds  of  6  ? 

12.  What  is  1  half  of  8?     10?     12?     14?    16?    18? 

13.  If  3  quarts  of  strawberries  cost  18  cents,  what 
will  1  quart  cost  ?     2  quarts  ? 

14.  What  is  1  third  of  18  ?     1  half  of  18  ? 

15.  If  4  pounds  of  raisins  cost  8  dimes,  what  part  of 
8  dimes  will  1  pound  cost  ?    2  pounds  ?    3  pounds  ? 

1 6.  What  is  1  fourth  of  8  ?   of  12  ?   of  16  ?   of  20  ? 

17.  What  is  1  fifth  of  15?   of  10?   of  20?   of  30  ? 

1 8.  If  1  fifth  of  15  is  3,  what  is  2  fifths  of  15  ?     3 
fifths?     4  fifths?     6  fifths?     8  fifths  ? 

19.  What  is  1  sixth  of  12? 


58  FRACTIONS. 

20.  What  is  2  sixths  of  12?  3  sixths?  4  sixths?  5  sixths? 

21.  What  is  1  seventh  of  21? 

22.  If  1  seventh  of  21  is  3,  what  is  2  sevenths  of  21  ? 
3  sevenths  ?     4  sevenths  ?     5  sevenths  ? 

23.  If  1  pound  of  candy  cost  12  cents,  what  part  of  a 
pound  can  you  buy  for  1  cent  ?  for  2  cents  ?  for 

3  cents  ?   for  5  cents  ?   for  8  cents  ? 

24.  If  a  coat  cost  $20,  and  a  pair  of  pantaloons  1  fourth 
as  much,  how  much  will  the  pantaloons  cost  ? 

25.  If  7  barrels  of  cider  cost  $28,  what  part  of  $28 
will  1  barrel  cost  ?  4  barrels  ?  6  barrels  ?  5  barrels  ? 

26.  What  is  1  seventh  of  $28  ?   2  sevenths  of  $28  ? 

4  sevenths  ?   5  sevenths  ?  7  sevenths  ?  6  sevenths  ? 

27.  If  1  pound  of  cheese  cost  6  cents,  how  much  will 
1  third  of  a  pound  cost  ?     2  thirds  ? 

28.  If  12  lemons  cost  36  cents,  what  part  of  36  cents 
will  1  lemon  cost  ?    2  ?    4  ?    5  ?    8  ?    10  ?    9  ?    7  ? 

29.  What  is  1  twelfth  of  36  ?     2  twelfths  of  36  ?     4 
twelfths  ?     5  twelfths  ?    6  twelfths  ?    9  twelfths  ? 

30.  What  do  you  understand  by  1  third  ?    2  thirds  ? 

ANSWER. — When  a  thing  has  been  divided  into  three 
equal  parts,  one  of  these  parts  is  called  1  third,  and  2  of 
these  parts  are  called  2  thirds. 

31.  What  do  you  understand  by  1  half? 

32.  What  do  you  understand  by  1  fourth?  2  fourths ? 

33.  What  do  you  understand  by  1  fifth  ?    2  fifths? 

34.  How  many  thirds  make  a  whole  one  ? 

35.  How  many  fourths  in  1  ? 

36.  What  do  you  understand  by  2  sixths  ?    4  sixths  ? 

37.  What   do  you   understand  by   3    sevenths  ?     2 
sevenths  ?     4  sevenths  ?     5  sevenths  ? 

38.  How  many  sixths  in  1  ? 

39.  How  many  ninths  in  1  ? 

40.  How  many  eighths  in  1  ? 

41.  How  many  sevenths  in  1  ? 

42.  How  many  tenths  in  1  ? 

43.  How  many  twentieths  in  1  ? 


FRACTIONS.  59 

44.  What   do   you   understand   by   7   twelfths  ?      6 
twelfths  ?     9  twelfths  ?     8  twelfths  ? 

45.  James  had  9  marbles,  and  Jacob  had  2  thirds  as 
many ;  how  many  had  Jacob  ? 

ANALYSIS. — If  James  has  9  marbles,  and  Jacob  2  thirds 
as  many,  Jacob  must  have  2  thirds  of  9  marbles.  1  third 
of  9  marbles  is  3  marbles,  and  2  thirds  are  2  times  3  mar- 
bles, which  are  6  marbles,  Jacob's  number. 

46.  Mary  bought  12  needles,  and  Sarah  bought  2 
thirds  as  many ;  how  many  did  Sarah  buy  rt 

47.  Rachel  has  12  primers,  Mary  3  fourths  as  many, 
and  Anthony  2  thirds  as  many  as  Mary ;  how 
many  have  Mary  and  Anthony  respectively  ? 

48.  Albert  is  15  years  old,  and  Ebenezer  is  4  fifths  as 
old ;  how  old  is  Ebenezer  ? 

49.  Augustus    has    40   cents,   and   Augusta    has    5 
eighths  as  many ;  how  many  has  she  ? 

50.  Morgan  had  36  marbles,  and  gave  4  sixths  of 
them  to  Martin ;  how  many  did  he  give  to  Mar- 
tin, and  how  many  had  he  left  ? 

51.  Moses  had   24  fire-crackers,  and  Nathan  has  7 
sixths  as  many ;  how  many  has  Nathan  1 

52.  Mifnin  had  45  cents,  and  Matthew  had  5  ninths 
as  many  ;  how  many  had  Matthew  ? 

53.  Dubois  is  20  years  old,  and  his  father  is  9  fifths 
as  old  ;  what  is  his  father's  age  3 

54.  A  farmer  had  84  sheep,  and  a  wolf  killed  1  third 
of  them  ;  how  many  had  he  remaining  I 

55.  In  a  certain   school   there   are  12  girls,  and  7 
fourths  as  many  boys ;  required  the  number  of 
boys,  and  the  number  of  boys  and  girls  together. 

56.  In  a  recitation  36  questions  were  answered,  and 
1  ninth  of  them  answered  wrong ;    how  many 
were  correctly  answered  ? 

57.  4  fifths  of  all  the  words  given  out  in  a  lesson 
were  spelled  correctly,  and  8  were  misspelled ; 
of  how  many  words  did  the  lesson  consist  ? 


FRACTIONS. 

58.  Montgomery  bought  9  walnuts  for  1  cent;  what 
part  of  a  cent  did  1  cost  ?   2  ?    3  ?    6  ?   7  ?   9  ? 

59.  A  colt  was  bought  for  $60,  and  sold  for  7  fifths 
of  what  it  cost ;  how  much  was  the  gain  ? 

60.  A.  received  $140  for  14  weeks'  labor,  and  paid 
1  fifth  of  it  for  board  ;   how  much  did  he  save 
each  week  ? 

6 1.  How  many  are  4  fifths  of  75  ? 

62.  How  many  are  7  eighths  of  24  ? 

63.  Mr.  A.'s  wife  is  40  years  old,  and  9  eighths  of  her 
age  equals  his ;  what  is  his  age  ? 

64.  "What  is  2  ninths  of  36  ?     4  ninths  ?     3  fourths  ? 
4  sixths  ?     5  sixths  ?     4  twelfths  ?     9  twelfths  ? 

65.  How  many  are  3  fourths  of  48  ?     4  sixths  ?     5 
eighths  ?  7  eighths  ?  6  eighths  ?  5  sixths  ?  2  thirds  ? 

66.  3  ninths  of  27  are   how  many  ?     4  ninths  ?     7 
ninths  ?     8  ninths  ?     2  thirds  ? 

67.  3  fourths  of  24  are  how  many  times  3  ? 

ANALYSIS. — 1  fourth  of  24  is  6,  and  3  fourths  are  3 
times  6,  which  are  18.     18  are  6  times  3. 

68.  5  sevenths  of  63  are  how  many  times  3  ? 

69.  3  eighths  of  64  are  how  many  times  6  ? 

70.  9  thirds  of  18  are  how  many  times  3  2 
71.4  fifths  of  25  are  how  many  times  2  ? 

72.  6  ninths  of  18  are  how  many  times  6  ? 

73.  7  ninths  of  90  are  how  many  times  2  ? 

74.  4  thirds  of  39  are  how  many  times  2  ? 

75.  15  seventeenths  of  34  are  how  many  times  6  ? 

76.  How  many  times  17  are  17  eighteenths  of  36  ? 

77.  How  many  times  8  are  12  thirteenths  of  26  ? 

78.  How  many  times  5  are  10  thirds  of  36  ? 

79.  How  many  times  4  are  2  thirds  of  27,  —  2  ? 

80.  How  many  times  6  are  3  halves  of  48,  +12  ? 

8 1.  Stephen  having  40  apples,  gave  3  fifths  of  them 
to  one  companion,  and  3  eighths  of  them  to  an- 
other ;  how  many  had  he  remaining  ? 

82.  A.  had  $120;  1  third  of  it  he  spent  for  a  watch, 


FRACTIONS.-  61 

1  fourth  of  it  for  a  suit  of  clothes,  and  3  tenths 
of  it  for  a  sleigh ;  how  much  had  he  remaining  ? 

83.  B.,  being  asked  the  cost  of  his  hat,  replied,  2 
thirds  of  $30  is  4  times  its  cost ;  required  its  cost. 

84.  14  ninths  of  $27  is  equal  to  7  times  the  cost  of 
a  pair  of  boots ;  required  the  cost  of  the  boots. 

85.  An  individual,  having  $90  on  interest,  received 

2  forty-fifths  of  the  principal  for  the  interest; 
how  much  interest  did  he  receive  ? 

86.  The  interest  received  on  $360,  was  1  eighteenth 
of  the  principal ;  how  much  was  the  interest  ? 

87.  B.  is  worth  $2000,  and  3  fourths  of  his  fortune  is 

3  times  A.'s ;  required  A.'s  fortune. 

88.  3  eighths  of  the  number  of  hours  in  a  day,  is  3 
times  the  number  of  hours  I  work ;  how  many 
hours  do  I  work  ? 

89.  A  pole,  whose  length  is  16  feet,  is  in  the  air  and 
water ;  and  3  fourths  of  the  whole  length,  less  4 
feet,  equals  the  length  in  the  air ;   required  the 
length  in  the  water. 

90.  3  fifths  of  $2000,  +$120,  equals  B.'s  fortune; 
how  much  is  B.  worth  ? 

91.  The  building  of  a  house  cost  $560,  and  4  sevenths 
of  this,  +  $80,  is  1  tenth  of  the  cost  of  the  farm  on 
which  it  stands ;  required  the  cost  of  the  farm. 

92.  5  eighths  of  72, +  13,  are  how  many  times  2? 

93.  The  interest  on  $960  for  5  years,  was  equal  to  1 
third  of  the  principal ;  how  much  was  the  yearly 
interest  ? 

94.  What  will  2  thirds  of  12  pounds  of  coffee  cost,  at 
13  cents  a  pound  ? 

95.  What  will  3  fourths  of  a  gallon  of  alcohol  cost,  at 
9  cents  a  pint  ? 

96.  What  will  1  sixteenth  of  a  bushel  of  flax-seed 
cost,  at  5  cents  a  pint  ? 

97.  How  much  will  7  fifteenths   of  30   pine-apples 
cost,  at  2  dimes  each  2 


62  .FRACTIONS. 

98.  How  much  will  7  ninths  of  a  hogshead  of  molas- 
ses cost,  at  4  dimes  a  gallon  ? 

99.  How  many  cents  will  3  fifths  of  100  oranges  cost, 
at  1  half  dime  each  ? 

100.  If  1  pennyweight  of  gold  cost  $1,  how  much 
will  2  fifths  of  an  ounce  cost  ? 

101.  What  will  be  the  cost  of  2  thirds  of  36  pounds 
of  butter,  at  2  dimes  a  pound  ? 

1 02.  2  thirds  of  24,  +3  fourths  of  16,  are  how  many 
times  7  ? 

103.  2  thirds  of  30,  +3  fifths  of  40,  are  how  many 
times  8  ? 

104.  3  sevenths  of  21,  +  3  eighths  of  40,  are  how 
many  times  6  ? 

105.  How  far  can  I  walk  in  3  eighths  of  a  day,  at  the 
rate  of  3  miles  an  hour  ? 

1 06.  If  Marcus  earn  1  dime  in  an  hour,  how  many 
cents  can  lie  earn  in  3  eighths  of  a  day  \ 

107.  If  a  horse  travel  10  miles  in  an  hour,  how  many 
times  10  miles  can  he  travel  in  5  twelfths  of  a 
day? 

1 08.  How  much  will  1  quart  of  gin   cost,  if  1  gill 
cost  1 5  cents  ? 

109.  How  many  dollars  will  4  sixths  of  a  pound  of 
gold  cost,  if  1  pennyweight  cost  10  dimes  ? 

no.  How  many  Eagles  will  25  fourths  of  a  gallon  of 
brandy  cost,  at  1  half-dime  a  gill  2 


FRACTIONS.  63 

LESSON     XXVIII. 

1.  If  1  third  of  an  orange  cost  2  cents,  what  will  1 
orange  cost  ? 

ANALYSIS. — If  1  third  of  an  orange  cost  2  cents,  3  thirds, 
or  1  orange,  will  cost  3  times  2  cents,  which  are  6  cents. 

2.  If  1  half  of  a  pound  of  raisins  cost  8  cents,  what 
will  1  pound  cost  ? 

3.  Bought  1  third  of  a  barrel  of  sugar  for  $3 ;  how  much 
will  2  thirds  of  a  barrel  cost,  at  the  same  rate  ? 

4.  If  1  third  of  a  pound  of  pork  cost  5  cents,  how 
much  will  2  pounds  cost  ? 

5.  2  is  1  third  of  what  number  ? 

ANALYSIS. — If  1  third  of  some  number  is  2,  3  thirds, 
which  is  that  number,  are  3  times  2,  which  are  6. 

6.  5  is  1  half  of  what  number? 

7.  If  1  fourth  of  a  lemon  cost  2  cents,  what  will  1  cost  ? 

8.  If  1  fourth  of  a  melon  cost  5  cents,  what  will  1  cost  ? 

9.  3  is  1  fourth  of  what  number? 
i  o.  7  is  1  third  of  what  number  ? 

11.  12  is  1  fifth  of  what  number  ? 

12.  7  is  a  fourth  of  wrhat  number  ? 

13.  What  will  4  fifths  of  a  pound  of  cinnamon  cost, 
if  1  fifth  of  a  pound  cost  5  cents  ? 

14.  If  1  fifth  of  a  yard  of  cloth  cost  $2,  what  will  a 
yard  cost  ? 

15.  If  1  sixth  of  a  gallon  of  vinegar  cost  2  cents, 
what  will  1  gallon  cost  ? 

1 6.  A  man,  being  asked  the  value  of  his  horse,  said, 
1  eighth  of  its  value  is  $12 ;  what  wras  its  value  \ 

17.  A  man  gave  15  cents  for  his  lodging,  which  was 
1  seventh  as  much  as  his  breakfast   cost ;    how 
much  did  his  breakfast  cost  ? 

1 8.  Bought  1  eighth  of  a  yard  of  cloth  for  4  dimes; 
wThat  will  a  yard  cost  at  this  rate  ? 

19.  If  1  tenth  of  a  yard  of  cloth  cost  47  cents,  hovr 
much  is  the  price  of  a  yard  \ 


64  FRACTIONS. 

20.  What  will  1  yard  of  cloth  cost,  if  1  ninth  of  a 
yard  cost  5  cents  ? 

21.  What  will  1  bushel  of  corn  cost,  if  1  seventh  of  a 
bushel  cost  5  cents  ? 

22.  What  will  a  hogshead  of  molasses  cost,  if  1  eighth 
of  a  hogshead  cost  $8  ? 

23.  What  will  be  the  cost  of  2  cords  of  wood,  if  1 
eleventh  of  a  cord  cost  30  cents  ? 

24.  If  1  twelfth  of  the  distance  from  Albany  to  Wil- 
braham  is  9  miles,  what  is  the  entire  distance  ? 

25.  9  is  1  tenth  of  what  number  ? 

26.  15  is  1  seventh  of  what  number  ? 

27.  16  is  1  fifth  of  what  number? 

28.  12  is  1  fifth  of  6  times  what  number  ? 

29.  15  is  1  sixth  of  5  times  what  number  ? 

30.  18  is  1  fourth  of  6  times  what  number  ? 

31.  10  is  1  eighth  of  20  times  what  number? 

32.  15  is  1  seventh  of  5  times  what  number? 

33.  20  is  1  eighth  of  16  times  what  number? 
34»  30  is  1  third  of  6  times  what  number  ? 

35.  A  boy's  hat  cost  $3,  which  was  1  fifth  of  the  cost 
of  his  coat ;  the  cost  of  the  coat  is  required. 

36.  Mr.  B.'s  saddle  cost  $9,  which  was  1  fortieth  of  6 
times  the  cost  of  his  horse ;  the  cost  of  the  horse 
is  required. 

37.  Henry  gave  5  cents  for  a  piece  of  pie,  which  was 
1  twentieth  of  4  times  as  much  as  his  breakfast 
cost ;  what  was  the  cost  of  'his  breakfast  ? 

38.  A  man,  being  asked  his  age,  answered  that  his 
youngest  son's  age,  which  was  12  years,  was  just 
1  twelfth  of  3  times  his  age ;  required  the  father's 


39.  Mrs.  B.'s  shawl  cost  $9,  which  was  1  tenth  of  3 
times  the  cost  of  her  dress ;  what  was  the  cost  of 
her  dress  ?   . 

40.  John  said  to  James,  who  is  now  10  years  old, 
your  age  is  1  eighth  of  4  times  my  age ;  how  old 
is  John  ? 


FRACTIONS. 


LESSON     XXIX. 

1.  If  2  thirds  of  a  melon  cost  4  cents,  what  will  1 
melon  cost  ? 

ANALYSIS.  —  If  2  thirds  of  a  melon  cost  4  cents,  1  third 
will  cost  1  half  of  4  cents,  which  is  2  cents,  and  3  thirds, 
which  is  1  melon,  will  cost  3  times  2  cents,  which  are 
6  cents. 

2.  If  2  thirds  of  an  orange  cost  5  cents,  what  will  1 
orange  cost  ? 

3.  If  3  fourths  of  a  pound  of  cotton  cost  9  cents,  what 
will  1  pound  cost  ? 

4.  If  4  thirds  01  a  pound  of  spice  cost  16  cents,  what 
will  1  pound  cost  ? 

5.  If  3  fourths  of  a  pound  of  cinnamon  cost  12  cents, 
what  will  1  pound  cost  ? 

6.  If  $4  will  buy  2  tilths  of  a  barrel  of  fish,  what  will 
1  fifth  of  a  barrel  cost  'i 

7.  What  will  1  yard  of  cloth  cost,  if  4  sixths  of  a 
yard  cost  120  cents  ? 

8.  What  will  1  hogshead  of  molasses  cost,  if  5  sevenths 
of  a  hogshead  cost  $15  ? 

9.  8  is  2  thirds  of  what  number? 

ANALYSIS.  —  If  2  thirds  of  some  number  is  8,  1  third  of  that 
number  is  1  half  of  8,  which  is  4;  and  3  thirds,  which  is  that 
number,  are  3  times  4,  which  are  12.  Therefore,  8  is  2  thirds 
of  12. 

REMARK.  —  Representing  the  conditions  and  solutions  of  ques- 
tions by  symbols,  will  aid  young  pupils  in  comprehending  the 
more  difficult  parts  of  arithmetical  analysis.  The  condition  and 
analysis  of  the  preceding  question  may  be  represented,  thus  : 

s 
If      fa      '       '       '  =  |  of  some  number  =  8, 


=  £  of  that  number  =  4, 

|.  which  is  that  number.  =  12. 

u  '  ' 


66  FRACTIONS. 

10.  12  is  2  thirds  of  what  number? 
TI.     4  is  2  thirds  of  what  number? 

1 2.  10  is  2  sevenths  of  what  number  ? 

13.  9  is  3  fourths  of  what  number  ?  - 

14.  12  is  3  fourths  of  what  number? 

15.  12  is  6  elevenths  of  what  number? 

1 6.  14  is  7  eighths  of  what  number? 

17.  14  is  2  sevenths  of  what  number? 

1 8.  6  is  3  tenths  of  what  number? 

19.  9  is  3  sevenths  of  what  number? 

20.  15  is  5  sixths  of  what  number? 

21.  15  is  3  halves  of  what  number? 

22.  18  is  9  eighths  of  what  number? 

23.  .20  is  5  thirteenths  of  what  number  ? 

24.  24  is  8  fifths  of  what  number  ? 

25.  26  is  13  ninths  of  what  number? 

26.  2  thirds  of  12  is  2  fifths  of  what  number? 

27.  3  fourths  of  12  is  3  eighths  of  what  number? 

28.  3  fourths  of  8  is  2  sevenths  of  what  number  ? 

29.  3  fifths  of  25  is  5  fourths  of  what  number? 

30.  2  sevenths  of  14  is  4  ninths  of  what  number? 

31.  4  sevenths  of  21  is  3  tenths  of  what  number? 

32.  2  thirds  of  15  is  5  fourths  of  what  number? 

33.  7  eighths  of  48  is  3  halves  of  what  number? 

34.  8  ninths  of  36  is  4  fifths  of  what  number? 

35.  7  thirds  of  18  is  3  fifths  of  what  number? 

36.  A  watch  cost  $16,  and  3  halves  of  the  cost  of  the 
watch  was  8  thirds  of  the  cost  of  the  chain ;  what 
was  the  cost  of  the  chain  ? 

37.  A  horse  was  sold  for  $96,  which  was  8  sevenths 
of  what  it  cost ;  what  was  the  cost  of  the  horse  ? 

38.  In  a  certain   school   there   are  36  girls,  and  5 
fourths  of  the  number  of  girls  equals  3  fifths  of 
the  number  of  boys;  how  many  boys  wero  there 
in  the  school  ? 

39.  Mary  is  14  years  old,  and  4  sevenths  of  IT 
is  2  thirds  of  Hezeki^h's  age;  what  is  h: 


FRACTIONS. 


67 


40.  A  piece  of  cloth  containing  12  yards  was  sold  for 
§60,  which  was  5  fourths  of  the  cost ;  how  much 
did  it  cost,  and  what  was  the  gain  on  each  yard  ? 

41.  A.  has  48  geese,  and  3  fourths  of  his  number  is 
equal  to  9  sevenths  of  B.'s  number;  how  many 
geese  has  B.  ? 

42.  The  head  of  a  fish  is  12  inches  long,  and  3  fourths 
of  the  length  of  the  head  is  3  fifteenths  of  the  length 
of  the  body  ;  required  the  length  of  the  fish. 

43.  A  farm  was  sold  for  §1200,  which  was  only  6 
sevenths  of  what  it  was  worth ;  how  much  was 
lost  by  the  bargain  ? 

44.  $48  is  3  fifths  of  the  cost  of  12  yards  of  cloth  ;  for 
what  must  it  be  sold  a  yard  to  gain  $16  on  the 
whole  ? 

45.  A  man  gave  $60  for  a  suit  of  clothes,  which  was 
1  fifth  of  his  yearly  income ;    1  sixth  of  the  re- 
mainder he  spent  for  a  watch,  and  what   then 
remained  was  4  fifths  of  his  brother's  yearly  in- 
come.    What  was  the  yearly  income  of  each  2 


LES 

SON     XXX. 

1 

half 

is 

written 

thus, 

i- 

1 

third 

is 

written 

thus, 

1 

fourth 

is 

written 

thus, 

i 

1 

sixth 

is 

written 

thus, 

J- 

1 

seventh 

is 

written 

thus, 

f 

2 

thirds 

is 

written 

thus, 

f 

3 

fourths 

is 

written 

thus, 

I- 

7 

eighths 

is 

written 

thus, 

|. 

9 

tenths 

is 

written 

thus, 

5 

sevenths 

is 

written 

thus, 

f 

2 

fifths 

is 

written 

thus, 

i 

5 

thirds 

is 

written 

thus, 

1- 

&c. 


68  FRACTIONS. 

.»" 

REMAKK. — The  above  expressions  are  called  fractions.  The 
figure  above  the  short  horizontal  line  is  called  the  numerator, 
and  the  figure  below  the  line  is  called  the  denominator.  For 
example,  in  the  fraction  |- ,  the  3  is  the  numerator,  and  the  4  is 
the  denominator. 

The  denominator  of  a  fraction  shows  into  how  many  equal 
parts  the  thing  is  divided ;  and  the  numerator  shows  how  many 
of  these  pails  are  taken. 

j.  If  you  cut  an  orange  into  3  equal  parts,  what  is  1 
of  these  parts  called  ? 

2.  If  a  lemon  be  cut  into  4  equal  pieces,  what  will  1 
of  these  pieces  be  called  ?    2  pieces  ?    3  ?   4  ? 

3.  If  a  bushel  of  apples  be  divided  into  6  equal  parts, 
what  will  1  of  these  parts  be  called  ?   33   4  ?    6  ? 

4.  If  a  basket  of  peaches  be  divided  in  8  equal  parts, 
what  will  3  of  these  parts  be  called  ?   5  ?    6  ?   7  ? 

5.  How  can  you  find  2  thirds  of  an  apple? 

6.  How  can  you  find  3  fourths  of  an  orange  ? 

7.  In  f  how  many  times  1  ? 

•  ANALYSIS. —  In  1  there  are  2  halves;  therefore,  1  half  the 
number  of  halves  equals  the  number  of  ones.  1  half  of  4  is 
2  ;  therefore,  f  equals  2. 


9- 
10. 
n. 

12. 

H. 

16. 


19. 
20. 

21. 


In 

f 

how 

many 

times 

1? 

In 

§ 

how 

many 

times 

1  ? 

In 

•V1 

how 

many 

times 

1? 

In 

-V* 

how 

many 

times 

1  ? 

In 

¥ 

how 

many 

times 

1? 

In 

1 

how 

many 

times 

1? 

In 

¥ 

how 

many 

times 

1? 

In 

9 
H 

how 

many 

times 

1  ? 

In 

¥ 

how 

many 

times 

1? 

In 

-V8 

how 

many 

times 

1? 

In 

¥ 

hovt 

many 

times 

1? 

In 

V 

how 

many 

times 

1? 

In 

1 

])OW 

many 

times 

1? 

In 

¥ 

how 

many 

times 

1  ? 

REDUCTION     OF     F  B A  C  T I O  N S  . 


22. 

In 

V 

how 

23- 

In 

V 

how 

24. 

In 

24 

4 

how 

25- 

In 

¥ 

how 

26. 

In 

I 

how 

27- 

In 

¥ 

how 

28. 

In 

¥ 

how 

29. 

In 

¥ 

how 

3°- 

In 

¥ 

how 

31- 

In 

¥ 

how 

32- 

In 

¥ 

how 

33- 

In 

¥ 

how 

34- 

In 

¥ 

how 

35- 

In 

H 

how 

36. 

In 

45 
l£ 

how 

37- 

In 

I! 

how 

38. 

In 

104 

how 

39- 

In 

¥ 

how 

40. 

In 

¥ 

how 

many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 
many 

REMARK. — This  is  called  reducing  fractions  to  whole  or  mixed 
numbers.  A  mixed  number  is  a  whole  number  with  a  fraction 
added  to  it.  Thus,  3£-  is  a  mixed  number. 

When  the  numerator  is  less  than  the  denominator,  the  value 
is  less  than  a  unit,  and  the  expression  is  called  a  proper  fraction. 
When  the  numerator  is  equal  to,  or  greater  than  the  denomina- 
tor, the  value  is  equal  to,  or  greater  than  a  unit,  and  the  ex- 
pression is  called  an  improper  fraction. 

41.  What  kind  of  a  fraction  is  it  called,  when  the 
numerator  is  less  than  the  denominator? 

42.  What  kind  of  a  fraction  is  it  called,  when  the 
denominator  is  greater  than  the  numerator  ? 

43.  When  is  the  value  of  a  fraction  greater  than  a  unit? 

44.  When  the  denominator  is  less  than  the  numera- 
tor, what  kind  of  a  fraction  is  it  called? 

4$.  What  kind  of  a  fraction  is  it  called,  when  the 
numerator  is  larger  than  the  denominator  ? 


times 

1? 

times 

1  ? 

times 

1? 

times 

1  ? 

times 

1? 

times 

1  ? 

times 

1? 

times 

1  ? 

times 

1? 

times 

1? 

times 

1? 

times 

1? 

times 

1? 

times 

1? 

times 

1? 

times 

1? 

times 

1? 

times 

1  ! 

times 

1? 

70 


ADDITION     O  F     F  K  A  C  T  1  O  JNT  8  . 


46. 

Reduce 

} 

to 

a 

mixed 

number. 

47- 

Reduce 

1 

to 

a 

mixed 

number. 

48. 

Reduce 

¥ 

to 

a 

mixed 

number. 

49- 

Reduce 

¥ 

to 

a 

mixed 

number. 

50. 

Reduce 

¥ 

to 

a 

mixed 

number. 

Si- 

Reduce 

¥ 

to 

a 

mixed 

number. 

52. 

Reduce 

¥ 

to 

a 

mixed 

number. 

53- 

Reduce 

!f 

to 

a 

mixed 

number. 

54- 

Reduce 

¥ 

to 

a 

mixed 

number. 

55- 

Reduce 

¥ 

to 

a 

mixed 

number. 

56. 

Reduce 

¥ 

to 

a 

mixed 

number. 

57- 

Reduce 

V 

to 

a 

mixed 

number. 

58. 

Reduce 

¥ 

to 

a 

mixed 

number. 

59- 

Reduce 

3_I 
6 

to 

a 

mixed 

number. 

60. 

Reduce 

¥ 

to 

a 

mixed 

number. 

LESSON     XXXI. 

1.  James  had  f  of  an  apple,  and  John  gave  him  \ 
more ;  how  many  had  he  then  ? 

2.  Mary  had  f  of  an  orange,  and  her  father  gave  her 
f  of  an  orange  more ;  how  many  had  she  then  ? 

3.  Robert  had  I  of  a  melon,  and  bought  f  of  another ; 
how  many  had  he  then  ? 

4.  Susan  had  f  of  a  pint  of  walnuts,  and  gave  f  of  a 
pint  to  her  sister ;  how  much  had  Susan  left  ? 

5.  James  bought  ±£-  of  a  pound  of  candy,  and  on  his 
way  home  ate  f  of  a  pound ;  how  much  had  he  left  ? 

6.  John  gave  ^  of  a  pound  of  raisins  to  James,  -f  of  a 
.    pound  to  Mary,  and  kept  |  of  a  pound  himself; 

how  many  fifths  had  he  at  first  ? 

7.  Mortimer  gave  -|  of  a  dollar  for  a  hat,  $1 1  for  a  vest, 
and  had  $3-|  remaining;  how  much  had  he  at  first  ? 

8.  Jane  had  5  pounds  of  cinnamon,  and  Harriet  had  2| 
pounds ;  how  many  more  had  Jane  than  Harriet  ? 


C.J     OF     FRACTIONS.  71 

9.  What  is  the  sum  of  f  of  a  dollar,  f  of  a  dollar, 

and  f  of  a  dollar  ? 

1  °-  I  +  1)   are  how  many  ? 

1  r  •  i  +  I  are  how  man J  • 

12-  I  +  f  are  how  many? 

1 3-  i$  +  A  are  how  many  $ 
14.  •     |  -f  |   are  how  many? 
I5-  V+  4  are  how  many? 
1 6.  J3*+  |  are  how  many? 
ll-  -^  +  ^  are  how  many  ? 
1 8.  f  +y  are  how  many? 
J9-  J  +  I  +  4  =  how  many? 

y  o      '      o            o                                     «/ 

2O-  f  H~  I  +  I  =  how  many  ? 

21  T7(J  +  -A+  :flr=  how  manJ^ 

22.  |  -f  f  +  | -  =  how  many  ? 

23-  9  ~  "I  are  how  many  ninths  ? 

24.  V~~V~  are  how  many? 

25-  V—  I  are  how  many  ? 

26.  23^ —  |   are  how  many? 

27-  ¥~~  I  are  how  many? 

28.  y  —  §   are  how  many? 

29-  ~¥~  f  are  how  many? 

30.  \9-— f  are  how  many? 

31  -496""~"V"  are  how  many? 

32.  -4E7-—  |   are  how  many? 

33.  i|— ^f  are  how  many? 
34«  |  +  J  ~  |  =  how  many? 
35-  I  +  |-  f  =  how  many? 
36.  |  4--Y--  f  =  how  many? 

37-  tt-i8+H=  how  man.7? 

38.  -|  of  60- f  of  24  =  how  many  ? 

39.  |  of  40— f  of  10  =  how  many  ? 

40.  I  of  15  + 1  of  9-|  of  12  =  how  many? 


72          MULTIPLICATION     OF    FRACTIONS. 


LESSON     XXXII, 

1.  At  f  of  a  cent  each,  what  will  2  apples  cost  ? 

ANALYSIS. — If  1  apple  cost  f  of  a  cent,  2  apples  will  cos< 
twice  f  of  a  cent,  which  are  f ,  or  1£  cents. 

2.  At  |  of  a  cent  each,  vrhat  will  5  apples  cost  ? 

3.  At  |  of  a  dime  a  pound,  what  will  10  pounds  of 
sugar  cost  ? 

4.  At   1|    dimes  a  pound,  how  many  cents  will    8 
pounds  of  starch  cost  ? 

5.  At  f  of  a  cent  each,  what  will  25  filberts  cost  ? 

6.  At  |  of  a  dime  each,  how  many  cents  will  8  chick- 
ens cost  ? 

7.  At  |  of  a  dollar  a  yard,  what  will  15  yards  of  linen 
cost? 

8.  If  a  man  spend  f  of  a  dollar  a  day,  how  much,  at 
this  rate,  will  he  spend  in  23  days  ? 

9.  If  a  man  receive  f  of  an  Eagle  in  a  week,  how 
many  dollars  will  he  receive  in  52  weeks  ? 

10.  If  1  pound  of  sugar  cost  \\  dimes,  what  will  12 
pounds  cost  ? 

11.  At  5 1  cents  a  pound,  what  will  6  pounds  of  soap 
cost  ? 

12.  At  9|  cents  a  pound,  what  will  8  pounds  of  pork 
cost? 

13.  At  6|  cents  each,  what  will  12  lemons  cost  ? 

14.  At  7§  cents  each,  what  will  20  rabbits  cost? 

15.  At  12J-  cents  a  dozen,  what  will  4  doz.  eggs  cost  \ 

1 6.  At  11 1  cents  a  pound,  what  will  6  pounds  of 
honey  cost  ? 

1 7.  At  $7|  a  bbl.,  what  will  10  bbl.  of  tobacco  cost  * 

18.  At  $9|  a  bbl.,  what  will  10  bbl.  of  pork  cost  ? 

19.  What  will  6  boxes  of  raisins  cost,  at  $3|  a  box  ? 


MULTIPLICATION     OF     FRACTIONS.  73 

20.  What  will  14  bushels  of  wheat  cost,  at  $1|  a 
bushel  ? 

21.  What  will  7  barrels  of  cider  cost,  at  $3f  a  barrel  ? 

22.  If  a  barrel  of  flour  cost  $4,  what  will  5-f  bbl.  cost? 

23.  5  times  4  and  f  of  4  are  how  many  ? 

24.  7  times  6  and  |  of  6  are  how  many  ? 

25.  9  times  7  and  f  of  7  are  how  many  ? 

26.  12  times  9  and  f  of  9  are  how  many  ? 

27.  5  times  10  and  |-  of  10  are  how  many  ? 

28.  13  times  4  and  f  of  4  are  how  many  ? 

29.  8  times  7  and  f  of  7  are  how  many  ? 

30.  10  times  13  and  fy  of  13  are  how  many  ? 
31.7  times  20  and  f  of  20  are  how  many  ? 

32.  How  many  are  4  times  |  ? 

33.  How  many  are  4  times  2f  ? 

34.  How  many  are  3  times  4|  ? 

35.  How  many  are  5  times  3f,  -f-£$ 

36.  How  many  are  7  times  9|,   f  f  ? 

37.  How  many  are  8  times  ISf,  —  f? 

38.  How  many  are  9  times  lOf ,  —  f  ? 

39.  How  many  are  6  times  12|,  +2j  ? 
to.  How  many  are  12  times  9|,  -f-f  ? 


LESSON     XXXIII. 

1 .  If  you  give  to  6  persons  each  f  of  a  dollar,  how 
many  dollars  will  be  given  to  all? 

2.  What  will  be  the  cost  of  4  yards  of  cloth,  at  |  of  a 
dollar  a  yard  ? 

3.  If  1  yard' of  cloth  cost  $1|,  what  will  10  yards  cost  3 

4.  How  many  oranges  will  it  require  to  give  to  ea<jh 
of  9  boys  1^  oranges  ? 

4 


74          MULTIPLICATION     OF     FRACTIONS. 

5.  How  many  barrels  of  flour  does  that  man  give 
away,  who  gives  to  each  of  12  beggars  §  of  a  barrel  ? 

6.  Anthony  gave  to  each  of  his  7  companions  |  of  a 
pound  of  candy,  and  had  |  of  a  pound  left ;  how 
many  pounds  had  he  at  first  ? 

7.  Thornton  gave  to  each  of  9  beggars  f  of  a  dollar, 
and  had  $7  remaining ;  how  much  had  he  at  first  ? 

8.  James  gave  ^  of  an  orange  to  Jackson,  T5^  to 
Joseph,  and  T%  to  John  ;  what  part  of  an  orange 
had  James  remaining  ? 

9.  Harmon  meeting  3  poor  women  and  5  poor  men, 
gave  to  each  woman  |  of  a  dollar,  and  to  each 
man  -J  of  a  dollar,  and  had  only  $4  remaining ; 
how  much  had  he  at  first  ? 

jo.  How  many  quarts  of  chestnuts  must  that  boy 
have,  who  gives  to  each  of  20  persons  -J-  of  a 
quart,  and  has  7  quarts  remaining  ? 

11.  Mary,  after  giving  to  each  of  her  12  companions 
as  many  pinks  as  she  had  roses,  which  were  2, 
had  no  flowers  remaining  but  her  roses;   how 
many  flowers  had  Mary  at  first  ? 

12.  What  will  1  quart  of  vinegar  cost,  if  1  pint  cost 

}of  a  cent  ? 
f  1  gill  of  molasses  cost  f  of  a  cent,  what  will  2 
quarts  cost  ? 

14.  If  2  pints  of  beans  cost  4  cents,  what  will  1  peck 
cost? 

15.  If  3  pecks  of  buckwheat  cost  96  cents,  what  will 
1  pint  cost  ? 

1 6.  "What  will  10  yards  of  silesia  cost,  if  1  yard  cost 
18f  cents  ? 

17.  How  many  cents  will  4f  yards  of  silk  cost,  if  1 ' 
yard  cost  6  dimes  ? 

1 8.  What  will  f  of  a  yard  of  muslin  cost,  if  1  yard 
cost  10  cents  ? 

19.  What  will  7  spools  of  thread  cost,  if  1  spool  cost 
7f  cents  ? 


MULTIPLICATION     OF     FRACTIONS.          75 

20.  What  will  8|  yards  of  silk  cord  cost,  at  6  cents  a 
yard  ? 

21.  If  a  boat  sail  1  mile  in  5  minutes,  in  what  time, 
at  the  same  rate,  will  it  sail  9-J  miles? 

22.  What  will  6f  yards  of  muslin  cost,  if  1  yard  cost 
8  cents  ? 

23.  What  will  5  pictures  cost,  at  8f  cents  each  ? 

24.  How  much  will  9f  barrels  of  cider  cost,  at  $4  a 
barrel  ? 

25.  What  will  12  hats  cost,  at  $3f  each  ? 

26.  What  will  5 1  melons  cost,  at  4  dimes  each  ? 

27.  What  will  be  the  cost  of  13  yards  of  bishop  lawn 
at  $1^  a  yard  ? 

28.  What  will  be  the  cost  of  8  glasses,  at  $15f  each? 

29.  What  amount  of  money  will  be  required  to  pur- 
chase 30  pounds  of  rice,  at  0-|  cents  a  pound  ? 

30.  What  will  be  the  cost  of  23  pounds  of  crackers, 
at  8  J  cents  a  pound  ? 

31.  What  will  9  barrels  offish  cost,  at  $12f  a  barrel? 

32.  If  a  man's  income  is  9J  dimes  in  1  hour,  how 
much  will  it  be  in  24  hours  ? 

33.  If  1  gold  pen  cost  $2f ,  how  much  will  6  cost  ? 

34.  How  many  pounds  of  meat,  at  5  cents  a  pound, 
can  you  buy  for  $3|-  ? 

35.  What  will  be  the  cost  of  3  quarts  of  nuts,  at  64 
cents  a  peck  ? 

36.  If  railroad  fare  is  5£  cents  a  mile,  what  is  the 
price  of  a  ticket  for  12  miles  ? 

37.  How  many  dollars,    dimes,    and   cents   will   12 
yards  of  cloth  cost,  at  62  cents  a  yard  ? 

38.  How  many  dollars  and  cents  will   4  pecks   of 

S -ass-seed  cost,  if  1  pint  cost  5  cents  ? 
ow  much  is  13  pounds  of  cotton  worth,  at  13| 
cents  a  pound  ? 

40.  How  many  cents  will  16  bushels  of  potatoes  cost, 
at  2 1  dimes  a  bushel  ? 


76          .MULTIPLICATION     OF     FRACTIONS. 

LESSON     XXXI Y. 

An  integer  is  any  whole  number. 

There  are  two  methods  of  multiplying  a  fraction  by  an  integer: 

RULE  I.— Multiply  the  numerator  by  the  integer. 

RULE  II. — Divide  the  denominator  by  the  integer. 

NOTE. — See  Stoddard's  New  Practical  Arithmetic,  page  95. 
Arts.  140  and  141. 

1 .  How  many  are  5  times  ^  ? 

ANALYSIS  IST. — 5  times  -^  are  -f-f,  or  8£. 
ANALYSIS  Zi>. — 5  times  T7¥  are  |,  or  3£. 

2.  How  many  are  3  times  *$-  ? 

3.  How  many  are  9  times  ^  ? 

4.  How  many  are  5  times  f -J  ? 

5.  How  many  are  6  times  f  J  ? 

6.  How  many  are  9  times  -fy  ? 

7.  How  many  are  9  times  ^  ? 

8.  How  many  are  7  times  f-f  ? 

9.  8  times  |f  are  how  many  ? 

10.  11  times  ^f  are  how  many? 

11.  13  times  Jf  are  how  many  ? 
12.2  times  J  are  how  many  ? 

13.  5  times  ^  are  how  many  ? 

14.  6  times  ff  are  how  many  ? 

15.  7  times  -||  are  how  many  ? 

1 6.  12  times  Jf  are  how  many? 

17.  How  many  times  5  are  8  times  |§  ? 

1 8.  How  many  times  12  are  9  times  -|-|  ? 

19.  How  many  times  8  are  11  times  ||  ? 

20.  How  many  times  100  are  25  times 

21.  How  many  times  20  are  35  times 

22.  5  times  -^  is  4  times  Mary's  age  ;  what  is  her 


MULTIPLICATION,    &€.,     OF    FRACTIONS.  77 


23.  13  times  J^-  equals  J-  of  the  number  of  dollars  a 
wagon  cost  ;  required  the  cost  of  the  wagon. 

24.  25  times  ^g0-  equals  ^--J-^-  of  the  number  of  men 
the  Mexican  General  Santa  Anna  had  at  the 
battle  of  Buena  Vista  ;  how  many  men  had  he  ? 

25.  6  times  %£$-  is  -^  of  the  number  of  men  he  had 
wounded  ;  how  many  men  were  wounded  ? 

26.  7  times  $££•  is  J  of  the  number  of  men  he  had 
killed  ;  how  many  men  were  killed  ? 

27.  4  times  4f^  is  ^  of  the  number  of  men  General 
Taylor  had  at  the  same  battle  ;  how  many  had  he  ? 

28.  9  times  ^-  is  -J-  of  the  number  of  men  he  had 
killed  ;  how  many  were  killed  ? 

29.  8  times  |f  is  ^  of  how  many  times  3  ? 

30.  4  times  -f  f  is  J  of  how  many  times  5  ? 

31.  A  boy  worked  12  months,  at  the  rate  of  $10f  a 
month  ;  how  much  did  his  year's  wages  amount  to  ? 

32.  If  2  quarts  of  beans  cost  48  cents,  what  will  1 
gill  cost  ? 

33.  What  will  3  oranges  cost,  at  f  of  a  cent  each  ? 

34.  A  piece  of  work  was  performed  in  90  hours,  by 
working  6  hours  a  day  ;  how  many  days  did  it 
take  ? 

35.  If  1  man  can  dig  a  ditch  in  15  days,  how  long- 
will  it  take  5  men  to  dig  it  ? 

36.  If  a  certain  quantity  of  provision  serve  a  family 
of  4  persons  16  days,  how  long  would  it  last  a 
family  of  8  persons  ? 

37.  If  8  men  can  perform  a  piece  of  work  in  56  days, 
in  how  many  days  can  112  men  do  the  same  ? 

38.  If  3  men  can  plow  18  acres  in  6  days,  in  how 
many  days  could  9  men  do  the  same  ? 

39.  4  men  can  mow  a  certain  field  in  (5J  days,  in  how 
many  days  could  5  men  perform  the  same  work  ? 

40.  How  many  kegs  of  butter,  at  $4  a  keg,  will  pay 
for  6  barrels  of  cider,  at  $3jj  a  barrel  ? 


78  MULTIPLICATION,    &C.,    OF    FRACTIONS. 

41.  A  merchant  bought  6  yards  of  cloth,  and  sold  it 
for  $20,  which  was  ^°  of  what  it  cost ;  what  did 
it  cost  a  yard  ? 

42.  Bought  36  yards  of  cloth,  and  sold  |  of  it  for 
$25,  which  was  f  of  what  it  cost ;   how  much 
would  I  have  gained  by  selling  the  whole  at  the 
same  rate  ? 

43.  7  men  in  f  of  a  day  can  earn  $10 ;   how  long 
would  it  take  1  man  to  earn  the  same  ? 

44.  James  is  3-|  years  of  age,  which  is  £  of  the  age 
of  Henry ;  and  Henry  is  9  times  as  old  as  George ; 
what  is  the   age  of  Henry  and  of  George   re- 
spectively ? 

45.  ^  of  36  is  3  times  J  of  what  number  ? 

46.  J  of  32  is  f  of  3  times  what  number  ? 

47.  f  of  60  is  f  of  2  times  what  number  ? 

48.  |  of  40  is  f-  of  as  many  dollars  as  Mr.  B.'s  horse 
cost ;  what  was  the  cost  of  his  horse  ? 

49.  A  person,  being  asked  his  age,  said,  that  f  of  80 
was  |  of  10  times  his  age ;  what  was  his  age  ? 

50.  Morgan  is  20  years  old,  and  -|  of  his  age  is  f  of 
the  age  of  his  brother;    what   is   his   brother's 


LESSON     XXX  Y. 

1.  How  many  thirds  are  there  in  3  ? 

ANALYSIS  IST. —  In  1  there  are  3  thirds,  and  in  3  there 
are  3  times  3  thirds,  which  are  f . 

ANALYSIS  SD. — In  1  there  are  3  thirds ;  therefore,  3  times 
the  number  of  whole  ones  equal  the  number  of  thirds. 
8  times  3  are  9.  Therefore,  in  3  there  are  f. 

2.  How  many  fourths  are  there  in  3  ? 

3.  How  many  halves  are  there  in  6  ? 

4.  How  many  fifths  are  there  in  4-  ?   in  5  ? 

5.  How  many  fifths  are  there  in  7  ?   in  8  '( 


MULTIPLICATION,    &c.,     OF    FRACTIONS.  79 

6.  How  many  sixths  are  there  in  4  ?   in  3  ?   in  5  ? 

7.  How  many  sevenths  are  there  in  2  ?   in  4  ?   in  6  ? 

8.  How  many  eighths  are  there  in  7  ?   in  4  ?   in  5  ? 

9.  How  many  fifteenths  are  there  in  2  ?  in  3  ?  in  6  ? 
jo.  How  many  tenths  are  there  in  4  ?   in  6  ?   in  7  ? 

1 1.  How  many  fourths  are  there  in  3  and  \  ? 

1 2.  How  many  thirds  are  there  in  4  and  \  \ 

13.  How  many  thirds  are  there  in  3  and  f  ? 

14.  How  many  halves  are  there  in  8  and  |-  ?    - 

15.  Reduce  6|  to  an  improper  fraction. 

1 6.  Reduce  9-|  to  an  improper  fraction. 

17.  Reduce  7f  to  an  improper  fraction. 

1 8.  Reduce  5|  to  an  improper  fraction. 

19.  Reduce  4-f  to  an  improper  fraction. 

20.  Among  how  many  men  can  5|-  bales  of  cotton  be 
distributed,  provided  each  receives  \  of  a  bale  ? 

21.  Among    how   many   boys    can    7f   oranges   be 
divided,  provided  each  receives  \  of  an  orange  ? 

•-22.  8  and  |  are  how  many  times  f  ? 

ANALYSIS. — 8  and  f  equal  \4-.  f  is  contained  in  ^  37  times. 

23.  9 1  are  how  many  times  f  ? 

24.  9|  are  how  many  times  |  ? 

25.  7|  are  how  many  times  |  ? 

26.  12|  are  how  many  times  -|  ? 

27.  7f  are  how  many  times  f  ? 

28.  7|-  are  how  many  times  |  ? 

29.  4|  are  how  many  times  |  ? 

30.  10|  are  how  many  times  f  ? 

31.  8 1  are  how  many  times  -f  ? 

32.  12f  are  how  many  times  f  ? 

33.  4  times  3J  are  how  many  times  §  ? 

34.  9  times  1|  are  how  many  times  |  ? 

35.  5  times  6|  are  how  many  times  f  ? 


80  DIVISION     OF     FRACTIONS. 

36.  8  times  8f  are  how  many  times  f  ? 

37.  6  times  2-f-  are  how  many  times  f  ? 

38.  A  boy  distributed  9§  apples  equally  among  his 
companions,  giving  to  each  -|  of  an  apple ;  how 
many  companions  had  he  ? 

39.  Homer  distributed    $12 f   equally   among  some 
poor  women,  giving  to  each   $1|;    how  many 
women  were  there  ? 

40.  Mary  gave  -|  of  a  pie  to  each  of  her  9  visitors ; 
how  many  pies  did  it  take  ? 

41.  Bought  8  yards  of  cloth,  at  $5|  a  yard;    how 
much  silk,  worth  $1 J  a  yard,  will  pay  for  it  ? 

42.  Bought  9  yards  of  cloth,  worth  $1|  a  yard,  and 
paid  for  it  with  raisins,  at  $1-|  a  box  ;  how  many 
boxes  did  it  take  ? 

43.  How  many  bushels  of  turnips,  at  $|  a  bushel,  can 
be  bought  for  8  bushels  of  apples,  at  $  |  a  bushel  ? 

.44.  How  many  apples,  at  |  of  a  cent  each,  can  be 
bought  for  6  oranges,  at  2-£  cents  each  ? 

45.  How  many  yards  of  cloth,  at  $-f  a  yard,  can  be 
bought  for  10  firkins  of  butter,  at  $5-§-  a  firkin  £ 

46.  How  many  geese,  at  $|  each,  can  be  bought  for 
li  ducks,  at  $f  each? 

47.  How  many  boxes  of  cheese,  worth  $2f-  a  box, 
may  be  had  tor  17  firkins  of  butter,  at  $1|  a  firkin  ? 

48.  How  many  barrels  of  flour,  at  $5|  a  barrel,  may 
be  had  for  17  bundles  of  cotton,  at  $1 J  a  bundle  ? 

49.  How  many  sheep,  at  $1J  a  head,  may  be  had  for 
8  calves,  at  $3|  each  ? 

50.  How  many  quarts  of  pease,  at  f  of  a  cent  a  pint, 
may  be  bad  for  12  qt.  of  molasses,  at  4J  cents  a  qt.  ? 

51.  Mary   and   Jane   together  picked   5  times   2^- 
quarts  of  strawberries,  and  shared  them  equally 
with  their  companions ;   how  many  companions 
bad  they,  provided  each  received  1  j  quarts  ? 


DIVISION     OF     FRACTIONS.  81 

LESSON     XXX  YI. 

LESSONS    XXXV    AND    XXXVI    COMBINED. 

There  are  two  methods  of  dividing  a  fraction  by  an  integer : 
RULE  IST.— Divide  the  numerator  by  the  integer. 
RULE  SD. — Multiply  the  denominator  by  the  integer. 
HP  See  Stoddard's  New  Practical  Arithmetic,  pages  95,  90. 
r.  If  2  yards  of  cloth  cost  $|,  what  will  1  yard  cost? 

ANALYSIS. — If  2  yards  of  cloth  cost  $  of  a  dollar,  1  yard 
will  cost  £  of  f  of  a  dollar,  which  is  f  of  a  dollar. 

2.  If  3  apples  cost  f  of  a  cent,  what  will  1  apple  co-st? 

3.  If  2  oranges  cost  |  of  a  cent,  what  will  1  orange 
cost? 

4.  If  3  yards  of  cord  cost  \%  of  a  cent,  what  will  1 
yard  cost  ? 

5.  If  2  pounds  of  sugar  cost  8|  (or  ^6-  cents),  what 
will  1  pound  cost  ? 

6.  If  2  pine-apples  cost  14J  cents,  what  will  1  pine- 
apple cost  ? 

7.  If  |  of  a  melon  is  worth  2  oranges,  how  much  is  1 
orange  worth  ? 

8.  If  3  apples  are  worth  2f  quinces,  what  is  1  apple 
worth  ? 

9.  How  many  times    7  are  ||  ? 

10.  How  many  times  13  are  7|  ? 

11.  How  many  times    7  are  9  J  ? 

12.  How  many  times  21  are  16-J? 

13.  How  many  times    8  are  33  f? 

14.  How  many  times    7  are  10 J? 

15.  How  many  times  11  are 

1 6.  How  many  times  18  are 

17.  How  many  times    3  are 

1 8.  How  many  times    9  are  7f  ? 

19.  How  many  times    6  are  6|  ? 

20.  How  many  times  lo  are 


82  DIVISION     OF     FRACTIONS. 


21.  If  9  oranges  are  worth  $^,  how  many  cents  is  1 
orange  worth  ? 

22.  If  4  boxes  of  figs  cost  |  of  an  Eagle,  how  many 
dollars  will  1  box  cost  ? 

23.  If  7  pounds  of  cheese  cost  $^,  how  many  cents 
will  1  pound  cost  ? 

24.  If  3  cakes  cost  -^  of  a  dime,  how  many  cents 
will  1  cake  cost  ? 

25.  If  4  pounds  of  chocolate  cost  4f  dimes,  how  many 
cents  is  that  a  pound  ? 

26.  What  will  1  portfolio  cost,  if  3  cost  -£$  of  an 
Eagle  ? 

27.  If  8  quarts  of  alcohol  cost  32  dimes,  how  many 
cents  will  2  gills  cost  ? 

28.  What  will  1  pound  of  sugar  cost,  if  4  pounds  cost 
18f  cents  ? 

29.  If  6  pounds  of  cheese  cost  31  J  cents,  what  will  1 
pound  cost  ? 

30.  If  12  eggs  cost  9|  cents,  what  will  be  the  cost  of 
1  egg  ? 

31.  If  7  yards  of  cloth  cost  $24J,  what  will  1  yard 
cost  '$ 

32.  If  5   silk  shawls   cost   $27^-,  how  much  will  1 
cost? 

33.  If  9  pairs  of  boots  cost  $32|,  how  much  is  that  a 
pair  ? 

34.  If  9  oranges  are  worth  30|  walnuts,  how  many 
walnuts  is  1  orange  worth  ? 

35.  A  boy  gave  8  apples  for  18f  marbles,  how  many 
marbles  did  he  get  for  1  apple  ? 

36.  A  boy  gave  7  cents  for  17^  crackers  ;  how  many 
did  he  get  for  1  cent  ci 

37.  Mary  gave  10  pins  for  23  J  chestnuts;  how  many 
did  she  get  for  1  pin  ? 

38.  If  3  yards  of  broadcloth  are  worth  18f  yards  of 
muslin,  how  many  yards  of  muslin  may  be  had 
for  1  yard  of  broadcloth  ? 


DIVISION      O  F     FRACTIONS.  83 

39.  If  Jolin  can  walk  13  miles  while  Josiah  is  walk- 
ing 32J  miles,  how  far  can  Josiah  walk  while 
John  is  walking  1  mile  ? 

40.  If  2  chestnuts  are  worth  -^  of  a  cent,  and  20 
chestnuts  are  worth  f  of  a  lemon,  how  many 
cents  is  1  lemon  worth  \ 

41.  If  2  oranges  cost  f  of  a  cent,  what  will  1  orange 
cost  ? 

ANALYSIS. — If  2  oranges  cost  |  of  a  cent,  1  orange  will 
cost  £  of  f  of  a  cent,  which  is  %  of  a  cent. 

42.  If  3  yards  of  linen  cost  $1 1,  what  will  1  yard  cost  1 

43.  If  7  yards  of  tape  cost  13§  cents,  what  will  1 
yard  cost  ? 

44.  If  2  pints  of  molasses  cost  If  dimes,  how  many 
cents  will  1  gallon  cost  ? 

45.  How  many  times  8  are  6J  ? 

46.  How  many  times  6  are  5|  ? 

47.  How  many  times  4  are  4J  ? 

48.  How  many  times  2  are  13J  ? 

49.  How  many  times  7  are  7f  ? 

50.  How  many  times  8  are  9  times  f  J  ? 

51.  How  many  times  3  are  6  times  lyi- 

ANALYSIS. — 1^|-  equals  ff.     6  times  -ff  are  ^>-.     3  is 
contained  in  -^,  ^-,  or  3f  times. 

52.  How  many  times  9  are  10  times 

53.  How  many  times  7  are    5  times 

54.  How  many  times  5  are  15  times 

55.  How  many  times  7  are  15  times  If-f  ? 

56.  How  many  times  5  are    3  times  2|  ? 

57.  How  many  times  0  are    4  times  5|? 

58.  If  If}  yards  of  cloth  are  worth  $2^,  what  is  1  yard 
worth  ? 

59.  If  6|  bundles  of  grapes  are  worth  40  cents,  how 
many  cents  is  1  bunch  worth  ? 

60.  If  3|  baskets  of  peaches  are  worth  $5J,  what  iV 
1  basket  of  pearlies  worth  ? 


FRACTIONS. 

LESSON     XXXVII. 

1.  What  is  j  of  2  ? 

ANALYSIS.--^-  of  1  is  | ;  if  $  of  1  is  £,  $  of  2  is  twice  4, 
which  are  f .     Therefore,  £  of  2  is  £  of  1. 

2.  What  is  |  of  4  ?  of  8  ? 

3.  What  is  J  of  2  ?  32  5  ?  7  ?   9  ? 

4.  What  is  -i-  of  *3  ?  52  7  ?  9  ?   11  ? 

5.  What  is  I  of  2  ?  3  ?  4  ?  7  ?   8  ? 

6.  What  is  J  of  2  ?  3  ?  5  ?  7  ?   9  ? 

7.  What  is  |  of  2  ?  3  ?  5  ?  4  ?   6  ?   9  ?   11  ? 

8.  What  is  £  of  2  ?  4  ?  3  ?  5  ?   6  ?   7  ?   9  ? 

9.  What  is  i  of  2?  4?  7?  0?   3?  12?   11? 

10.  What  is  ^  of  7  ?   2-   4?   6-   9?   ^   15? 

11.  If  2  apples  cost  3  cents,  what  will  1  apple  cost  ? 

ANALYSIS.— If  2  apples  cost  3  cents,  1  apple  will  cost  £ 
of  3  cents,  which  is  f ,  or  1£  cents. 

12.  If  2  apples  cost  5  cents,  what  will  1  apple  cost  ? 

13.  If  3  pens  cost  8  cents,  what  will  1.  pen  cost  ? 

14.  If  3  yards  of  tape  cost  14  cents,  what  will  1  yard 
cost  ? 

15.  If  5  barrels  of  flour  cost  $21,  what  will  1  barrel 
cost  ? 

1 6.  If  7  pecks  of  dried  apples  cost  23  dimes,  what 
will  1  peck  cost  ? 

17.  If  4  chickens  cost  9  dimes, what  will  1  chicken  cost? 

1 8.  What  will  1  pound  of  tamarinds  cost,  if  6  pounds 
cost  27  dimes  \ 

19.  What  will  1  barrel  of  flour  cost,  if  3  barrels  cost 
$25? 

20.  If  you  divide  7  bushels  of  wheat  equally  among 
5  persons,  how  much  will  each  receive  ? 

21.  Joshua  had  13  marbles,  and    Lewis   had   \  as 
many  -f  \  of  a  marble ;  how  many  had  Lewis  ? 


FRACTIONS.  85 

22.  A.  divided  3  barrels  of  flour  equally  among  11 
families ;  what  part  of  a  barrel  did  each  receive  ? 

23.  A  farmer  divided  5  bushels  of  rye  equally  among 
7  of  his  poor  neighbors;  what  part  of  a  bushel 
did  he  give  to  each  ? 

24.  Calvin  had  4  pints  of  nuts,  and   shared   them 
equally  with  6  of  his  companions ;  how  much  did 
each  receive  ? 

25.  Margaret,  having  7  quarts  of  raspberries,  shared 
them  equally  with  8  of  her  playmates;  what  part 
of  a  quart  did  each  receive  '* 

26.  What  will  1  pound  of  prunes  cost,  if  5  pound? 
cost  48  climes  ? 

27.  What  cost  2  boxes  of  figs,  at  29  climes  for  7  boxes ? 

28.  What  will  4  quarts   of  strawberries   cost,  if  9 
quarts  cost  7  dimes  ? 

29.  What  is  |  of  2  ? 

30.  If  ^  of  2  is  f ,  what  is  f  of  2  ? 

31.  What  is  |  of  5? 

ANALYSIS. — £  of  5  is  f ,  and  f  are  2  times  -|.  which  are 
¥,  or  % 

32.  What  is  |  of  3  ?   of  5  ?    63   7  ?   9  ?    11  ? 

33.  What  is  §  of  2  3   of  33   4  ?   9  ?    11  ?   132 

34.  What  is  f  of  2  ?   of  3  ?    5  ?   7  ?   9  ?   15  ? 

35.  What  is  £  of  3  ?   of  5  ?    8  ?   9  ?    12  ?   20  ? 

36.  What  is  I  of  4  ?   of  6  ?   8  ?   12  ?   11  ?  17  ? 

37.  What  is  f  of  3?   of  5?    C?   9?   10?   15? 

38.  What  is  ^T  of  2  ?   of  4?   5?   6?    10?   12? 

39.  What  is  &  of  2  ?   of  4  ?   33   9  ?   15  ?   21  ? 

40.  What  is  ^  of  7  ?   of  8  ?   9  ?   12  ?   15  3   25  ? 

41.  How  many  cents  will  §  of  a  pound  of  candy  cost, 
if  1  pound  cost  2  dimes  ? 

42.  What  will  be  the  cost  of  f  of  a  box  of  raisins,  if 
1  box  cost  $3  '( 

43.  What  will  be  the  cost  of  |  of  a  yard  of  cloth,  at 
7  dimes  a  varrl  ? 


SO  SIMPLE     PROPORTION. 

44.  If  a  ton  of  hay  cost  $10,  what  will  2f  tons  cost  ? 

45.  Jeremiah  is  91  years  old,  and  f  of  his  age  equals 
the  age  of  his  oldest  son  ;  how  old  is  he  8 

46.  Bought  24  yards  of  cloth  for  $48 ;   but,  being 
damaged,  I  sold  j  of  it,  at  $1|  a  yard,  and  the 
remainder  for  what  it  cost ;  how  much  did  1  lose  ? 

47.  Bought  14  yards  of  cloth,  and  sold  f  of  it,  at  $-2 
a  yard,  which  amounted  to  $2  less  than  the  whole 
cost ;  what  did  it  cost  a  yard  ? 

48.  A  horse  was  sold  for  $97,  which  was  If  times  as 
much  as  it  cost ;  what  did  the  horso  cost  ? 

49.  If  9  yards  of  cloth  cost  $17,  what  will  3  yards 
cost  ? 

50.  If  7  yards  of  cloth  cost  $25,  what  will  9  yards 
cost  ? 

51.  What  will  2  pounds  of  opium  cost,  if  5  pounds 
cost  $42 ? 

52.  If  5  pounds  of  indigo  cost  $32,  what   will   2 
pounds  cost '? 

53.  A  wagon  was  sold  for  $90,  which  was  f  of  what 
it  cost ;  how  much  did  it  cost  ? 

54.  Two  men  started  from  the  same  place,  and  trav- 
eled the  same  way ;  one  at  the  rate  of  92  miles  in 
10  hours ;  the  other  at  the  rate  of  l-j\y  miles  in  \ 
of  an  hour;    how  far  apart  will  they  be  in  2 
hours  ? 

55.  By  a  pipe  4f  gallons  of  water  ran  into  a  cistern 
in  1  minute ;  how  much  did  the  vessel  hold,  pro- 
vided it  was  filled  in  9  minutes  ? 

56.  If  7  men  can  perform  a  piece  of  work  in  13-f- 
days,  how  long  would  it  take  4  men  to  do  the 
same  2 

57.  If  5  persons  consume  a  barrel  of  flour  in  9  weeks, 
what  part  of  a  barrel  would  they  consume  in  5 
weeks  ? 

58.  If  a  man  earn  $J  in  a  day,  and  a  boy  $|,  how 
much  will  both  earn  in  6  days  ? 


SIMPLE     PROPORTION.  87 

59.  Anthony  spent  f  of  all  his  money,  and  the  re- 
mainder he  gave  for  8  yards  of  cloth,  at  $2f  a 
yard  ;  how  much  had  he  at  first  ? 

60.  From  a  piece  of  cloth  a  tailor  cut  5  garments, 
each  containing  3f  yards;   and  there  remained 
2f  yards  ;  how  many  yards  did  the  piece  at  first 
contain  ? 

61.  What  will  9  pounds  of  rice  cost,  if  7  pounds  cost 
43  cents  ? 

62.  An  individual,  after  spending  ^f  of  all  his  money, 
had  only  $40  remaining ;   how  much  had  he  at 
first? 

63.  An  old  lady  bought  30  eggs,  at  the  rate  of  2  for 
5  cents ;  what  did  they  cost  ? 

64.  How  much  will  13  pounds  of  coflfee  cost,  if  26 
pounds  cost  $7  ? 

65.  What  will  7  gallons  of  molasses  cost,  if  6  pints 
co;t  27  cents  \ 

66.  If  5  lamps  cost  $7J,  what  will  7  lamps  cost  ? 

67.  If  5  horses  can,  in  4f  days,  consume  20  bushels 
of  oats,  in  how  many  days  can  11  horses  consume 
the  same  ? 

68.  If  15  gold  pens  cost  $20,  what  will  5  of  them 
cost? 

69.  If  J  of  an  acre  of  land  be  worth  $14,  what  are 
10  acres  worth  ? 

70.  $25  is  |  of  the  cost  of  B.'s  watch ;  what  was  the 
cost  of  his  watch  ? 

71.  Mortimer's  hat  cost  $5,  and  |  of  the  cost  of  his 
hat  is  -fa  of  the  cost  of  his  coat ;  what  was  the 
cost  of  his  coat  ? 

72.  If  a  man  in  T45  of  a  day  walk  8  miles,  how  far 
can  he  walk  in  5  days  ? 

73.  From  a  piece  of  cloth  containing   25  yards,  a 
tailor  cut  8  suits  of  clothes,  each  containing  2j 
yards;  how  many  yards  remained  ? 

74.  If  a  man  can  cut  1  cord  of  wood  in  5  hours,  how 


88  SIMPLE     PROPORTION. 

many  cords  can  he  cut  in  4  days,  by  working  12 
hours  a  day  ? 

75.  A  man  bought  7  sheep,  at  the  rate  of  9  for  $5J ; 
what  did  they  cost  him  ? 

76.  A  boy  bought  13  oranges,  giving  9  apples  for  3 
oranges ;  how  many  apples  did  his  oranges  cost  ? 

77.  If  25  cents  buy  7  lemons,  how  many  cents  will  9 
lemons  cost  ? 

78.  |  of  45  equals  f  as  many  dollars  as  Andrew  has ; 
how  many  dollars  has  Andrew  ? 

79.  $30f  is  ^  of  all  the  money  A.  had ;   how  much 
money  had  A.  ? 

80.  What  will  3  pecks  of  flax-seed  cost,  if  3  pints 
cost  3  dimes  ? 

81.  What  will  1  quart  of  clover-seed  cost,  if  2  pecks 
cost  $3  and  2  dimes  ? 

82.  4J  times  7  is  J  of  what  number  ? 

83.  f  of  36  is  |  of  what  number  ? 

84.  |  of  36  is  -^-  times  what  number? 

85.  |  of  A.'s  ag^e  is  3  times  B.'s  age,  and  B  is  9  years 
old ;  what  is  A.'s  age  ? 

86.  An  individual,  being  asked  the  number  of  hours 
he   labored   each    day,   answered,   1J  times  the 
number  of  hours  in  a  day  is  3  times  as  many 
hours  as  I  labor ;  how  many  hours  did  he  labor 
each  day  ? 

87.  f  of  15  is  |  of  what  number  ? 

88.  f  of  21  is  1^  times  what  number  ? 
80.  4  of  24  is  1£  times  what  number  ? 

S  O  tJ 

90.  Wright  is  16  years  old,  and  If  times  his  age  is 
1|  times  Charles's  age.     How  old  is  Charles  ? 


SIMPLE     PROPORTION.  89 

LESSON     XXXYI1I. 

LESSONS   XXXIV,    XXXV,   AND   XXXVI    COMBINED. 

REMARK. — Pupils  must  exercise  their  judgment  to  employ 
the  shortest  of  the  methods  given  in  Lessons  XXXIV and  XXXVI, 
for  multiplying  and  dividing  fractions. 

1.  If  3  barrels  of  flour  cost  $13},  what  will  6  cost  ? 

ANALYSIS.— $13f  equals  $-5/.  If  3  barrels  of  flour  cost 
$-^5-,  6  barrels,  which  are  2  times  3  barrels,  will  cost  2  times 
|&  which  are  $A£,  or  $27£. 

2.  If  5  pounds  of  opium  cost  $27^,  what  will  20  cost  ? 

3.  If  3  caps  cost  $17|,  what  will  ^4  caps  cost? 

4.  How  many  apples  will  pay  for  9  oranges,  if  8  ap- 
ples are  worth  12|  oranges  ? 

ANALYSIS. — 12£  oranges  equal  -^  oranges.  If  -^  oranges 
are  worth  8  apples,  £  of  an  orange  is  worth  -^  of  8  apples, 
which  is  -£8¥,  or  %  or  an  apple ;  and  |,  or  1  orange,  are  worth 
5  times  -J-,  or  f-  of  an  apple,  and  9  oranges  are  worth  9  times 
|,  which  are  *£-,  or  5|  apples. 

REMARK. — In  solving  questions  in  Proportion,  never  seek 
the  value  of  a  unit  of  the  denomination  like  the  answer. 

5.  How  many  chestnuts  will  pay  for  9  walnuts,  if  7 
chestnuts  are  worth  lOf  walnuts  ? 

6.  If  8  barrels  of  flour  cost  $33f ,  what  will  20  bbl.  cost  ? 

7.  If  it  require  9|  yards  of  cloth  to  make  3  coats, 
how  many  yards  will  it  require  to  make  8  coats  ? 

8.  If  10  men  can  perform  a  piece  of  work  in  9f  days, 
how  long  will  it  take  8  men  to  perform  the  same  ? 

9.  "What  will  be  the  cost  of  6  sheep,  if  15  cost  $10  J  ? 

10.  If  1  person,  in  6  months,  consume  lO^g  bushels  of 
wheat,  how  much  will  13  persons  consume  ? 

n.  If  9^  cents  will  buy  4  peaches,  what  will  be  the 
cost  of  9  peaches  ? 

12.  If  $9^g  will  pay  for  5  weeks'  board,  how  many 
dollars  will  pay  for  8  weeks'  board  ? 

13.  If  6  orifices  fill  a  vessel  in  3|  hours,  how  many 
of  the  same  size  will  be  required  to  fill  it  in  -^  of 
an  hour  ? 


90  SIMPLE      PROPORTION. 

14.  If  9  men  can  build  a  boat  in  5|  days,  in  how 
many  days  could  6  men  build  it  ? 

15.  If  2  men  in  4  days  earn  $12,  how  many  dollars 
can  7  men  earn  in  the  same  time  ? 

1 6.  If  I  pay  17f  cents  for  riding  4  miles,  how  much 
must  I  pay  tor  riding  6  miles  ? 

1 7.  What  will  1  year's  board  cost,  at  $21f  for  4  weeks  ? 

1 8.  If  9  barrels  offish  cost  $54J,  what  will  27  cost  ? 

19.  How  many  dollars  will  1  barrel  of  tobacco  cost, 
if  17  barrels  cost  51 J  Eagles  ? 

20.  If  13  pounds  of  tea  cost  lOf  dimes,  what  will  5 
pounds  cost  ? 

21.  If  7f  tons  of  hay  keep  6  horses  through  the  winter, 
how  many  tons  will  keep  9  horses  the  same  time  ? 

22.  A  fox  is  40  rods  before  a  hound,  and  runs  3  rods 
to  the  hound  5  ;  how  many  rods  must  the  hound 
run  to  overtake  the  fox  ?   How  far  did  the  fox  run  ? 

23.  How  many  dollars  will  a  man  earn  in  14  days,  if 
he  earn  $3f  in  4  days  ? 

24.  A  merchant  bought  8  pieces  of  cloth,  each  piece 
containing  5  yards,  for  $32-|  ;   how  much  did  it 
cost  a  piece,  and  how  much  a  yard  ? 

25.  If  in  a  certain  time  6  horses  eat  14|  bushels  of 
oats,  how  many  bushels  will  8  horses  eat  in  the 
same  time  ? 

26.  A  boy  sold  3  lemons,  at  the  rate  of  6  for  8  cents ; 
how  much  did  he  receive  for  them  ? 

27.  A  boy  gave  4-J  cents  for  oranges,  at  the  rate  of  5 
oranges  for  7J  cents ;  how  many  did  he  buy  ? 

28.  If  a  piece  of  mahogany,  weighing  9  pounds,  is 
worth  $2|,  what  is  the  value  of  12  pounds,  at  the 
same  rate  ? 

29.  If  a  pole  8  feet  long  cast  a  shadow  4f  feet,  what 
will  be  the  length  of  the  shadow  of  a  pole  which 
is  15  feet  long,  at  the  same  time  of  day  ? 

30.  At  a  certain  time  of  day,  a  pole  5  feet  long  casts 
a  shadow  7 \  feet ;  what  is  the  length  of  that  pole 
which  at  the  same  time  casts  a  shadow  4^  feet  ? 


REDUCTION     OF     FRACTIONS.  91 

31.  If  it  require  $21^  worth  of  provisions  to  serve  8 
men  2  days,  how  many  dollars'  worth  will  serve 
5  men  4  days  ? 

32.  What  is  the  length  of  a  pole  the  shadow  of  which 
is  12  feet  long,  at  the  same  time,  a  pole  2|  feet 
in  length  casts  a  shadow  4  feet  long  ? 


LESSON     XXXIX. 

To  Reduce  a  fractien  to  a  fraction  having  a  given  denom- 
inator, 

Multiply  both  numerator  and  denominator  of  the  given 
fraction  by  a  number  that  will  cause  the  denominator  to  be- 
come the  required  denominator. 

[See  Lessons  xxxiv  and  xxxvi ;  also,  Stoddard's  New  Prac- 
tical Arithmetic,  page  96,  142,  Prop.  5.] 

1 .  |  is  how  many  eighths  ? 

ANALYSIS  1  ST.— There  are  f  in  1,  and  in  £  there  is  %  of 
|,  or  |,  and  in  £  there  are  3  times  f ,  or  f . 
ANALYSIS  2v. —  £  equal  f. 

2.  J  is  how  many  eighths  ? 

3.  ^  is  how  many  tenths  ? 

4.  |  is  how  many  sixths  ? 

5.  |  is  how  many  sixths  ? 

6.  |  and  j  are  how  many  sixths  ? 

7.  §  are  how  many  sixths  ? 

8.  |  are  how  many  twelfths  ? 

9.  |  are  how  many  twelfths  ? 

10.  |  are  how  many  eighteenths? 

11.  I  are  how  many  tenths  ? 

12.  |  are  how  many  tenths  ? 

13.  |  are  how  many  twentieths  ? 

14.  4  is  how  many  tenths  ? 

15.  Harris  gave  |  of  an  orange  to  his  sister;   how 
many  fifteenths  did  he  give  her  2 


92  ADDITION      AND     S  U  JB  T  JB  A  C  T  ION. 

1 6.  How  many  sixteenths  in  f  ? 

.       «•'  O 

1 7.  How  many  sixteenths  in  f  ? 

1 8.  How  many  sixteenths  in  |  ? 

19.  How  many  fourteenths  in  f  ? 

20.  How  many  fourteenths  in  f  ? 

21.  How  many  fourteenths  in  |-  ? 

22.  How  many  ninths  in  §  2 

23.  How  many  twentieths  in  -J  ? 

24.  How  many  fortieths  in  -J  ? 

25.  How  many  forty-ninths  in  f  ? 
26. ,  How  many  fifteenths  in  f  ? 

27.  A  man  gave  J  of  a  bushel  of  potatoes  to  one  poor 
woman,  and  -fy  of  a  bushel  to  another ;   what 
part  of  a  bushel  did  he  give  to  both  ? 

28.  How  could  you  divide  an  apple  so  as  to  give  f 
of  it  to  1  boy,  and  J  of  it  to  another  ? 

29.  |  -f  |  are  how  many  fifteenths  ? 

ANALYSTS.—  !  equals  T67,  and  f  equals  |f     TBj.  and  f§ 
are  |f,  or  1TV- 

30.  f-ff  are  how  many  twelfths? 

31.  |  +  j  are  how  many  eighteenths  ? 

32.  |  +|  are  how  many  twenty-fourths  ? 

33.  What  is  the  sum  of  f  and  ^  ? 

34.  What  is  the  sum  of  f  and  -|  ? 

35.  What  is  the  sum  of  f  and  |  ? 

36.  What  is  the  sum  of  J  and  ^  ? 

37.  What  is  the  sum  of  |  and  -|  ? 

38.  What  is  the  sum  of  f  and  |  ? 

39.  What  is  the  sum  of  ^  and  f  ? 

40.  What  is  the  sum  of  f  and  f  ? 

41.  What  is  the  sum  of  |  and  |  ? 

42.  What  is  the  sum  of  |  and  4-  ? 

43.  What  is  the  snm  of  f ,  £,  and  f  ? 

44.  What  is  the  sum  of  |,  |,  and  ^  ? 


OF      FRACTIONS.  93 


45.  From   |    subtract  J. 

46.  From    |   subtract  |. 

47.  From   f-   subtract  f. 

48.  From  2J  subtract  f. 

49.  From   4   subtract  -|. 

50.  From    3   subtract  f. 

51.  From    9    subtract  f. 

52.  From   5   subtract  |. 

53.  From   3   subtract  1^. 

54.  From   9   subtract  2f. 

55.  From   6   subtract  3|. 

56.  14—  3J  are  how  many  5 

57.  7—  2f  are  how  many? 

58.  9—  S-f-  are  how  many? 

59.  10—  3f  are  how  many? 

60.  12—  3 1  are  how  many? 

6 1 .  1 3 — 7T\  are  how  many  ? 

62.  9|—  4J  are  how  many? 

63.  7f —  5|  are  how  many? 

64.  3-J—  1^  are  how  many  ? 

65.  44—  If  are  how  many  ? 

66.  5|—  2|  are  how  many? 

67.  9f  —  7 §  are  how  many? 

68.  2|  -f-  3J—  |  =  how  many  ? 

69.  4|  +  5  j  — 2f  =  how  many  ? 

70.  3 1 +4-J-—  J  =  how  many  ? 

71.  9|+3|—  3  —how  many? 

72.  |  -f  |  —  |  —  how  many? 

73.  f  +  i+y— i=  how  many? 

74.  2J  are  how  many  times  -^g 

75.  8£  are  how  many  times 

76.  •£%  are  how  many  times 

77.  J  are  how  many  times 


1)1  K  E  D  U  C  T  I  O  N     OF     FRACTIONS. 

78.  |  are  how  many  times  T\  ? 

79.  1 J-  are  how  many  times  T3^  ? 

80.  -J  are  how  many  times  -^  ? 

8 1.  T\  are  how  many  times  -f$  ? 

82.  8 1  are  how  many  times  2£  ? 

83.  10-J  are  how  many  times  -^  ? 

84.  12  J  are  how  many  times  l|  ? 

85.  J  +  ^  +  J  is  how  much  less  than  a  whole  one  ? 

86.  y+ 1  + 1  is  how  much  less  than  a  whole  one  ? 

87.  A  lady  gave  |-  of  all  her  money  for  a  dress,  and  f 
of  it  for  a  shawl;    what  part  of  her  money  re- 
mained ? 

88.  ^  of  an  army  was  killed,  and  |  taken  prisoners; 
what  part  of  the  army  escaped  2 

89.  f  of  an  army  was  killed,  -|  taken  prisoners,  and 
500  escaped  ;  how  many  were  there  in  the  army  ? 

90.  |  of  the  length  of  a  pole  is  in  the  ground,  \  of  it 
in  the  water,  and  12  feet  in  the  air ;  what  is  the 
length  of  the  pole  ? 

91.  A  market  woman  sold  f  of  all  her  oranges  to  one 
man,  J  of  them  to  another,  and  then  had  only  9 
remaining  ;   how  many  had  she  at  first,  and  how 
'many  did  she  sell  to  each  ? 

92.  A  man,  after  spending   f  of  his  fortune,  found 
that  $20  was  |  of  what  he  had  remaining ;  what 
was  his  fortune  ? 

93.  A  hawk  caught  -|  of  Euphemia's  chickens,  a  cat 
killed  J  of  them,  ^  of  them  died,  and  she  had  13 
remaining ;  how  many  had  she  at  first,  and  how 
many  were  destroyed  by  the  hawk  and  cat  re- 
spectively ? 

94.  Said  A.  to  B.,  if  to  my  age  you  add  its  J  and  its 
|,  the  sum  will  be  38 ;  how  old  was  he  ? 

95.  A.  is  40  years  old,  and  f  of  his  age  is  f  of  twice 
as  much  as  his  wife's  age ;  how  old  is  his  wife  ? 


SEDUCTION     OF     F  K  A  C  T  I  O  N  S  .  9,3 

LESSON     XL. 

To  Reduce  a  fraction  to  its  lowest  terms, 

Divide  each  term  of  the  given  fraction  by  the  largest  num- 
ber that  is  contained  in  each  of  them  without  a  remainder. 

NOTE. — A  fraction  is  expressed  in  its  lowest  terms  when  no 
number  greater  than  1  will  divide  each  of  them  without  a 
remainder. 

1.  Keduce    f    to  its  lowest  terms. 

2.  Reduce    |    to  its  lowest  terms. 

3.  Reduce    -|    to  its  lowest  terms. 

4.  Reduce  -f%  to  its  lowest  terms. 

5.  Reduce  T%  to  its  lowest  terms. 

6.  Reduce  -Jf   to  its  lowest  terms. 

7.  Reduce  ||   to  its  lowest  terms. 

8.  Reduce  f  f  to  its  lowest  terms. 
9. -Reduce  ff  to  its  lowest  terms. 

10.  Reduce  f  |  to  its  lowest  terms. 

11.  Reduce  f-J  to  its  lowest  terms. 

1 2.  Reduce  j7^  to  its  lowest  terms. 

13.  Reduce  -ff  to  its  lowest  terms. 

14.  Reduce  f§  to  its  lowest  terms. 

15.  Reduce  {f  to  its  lowest  terms. 

1 6.  Why  does  the  value  of  the  fraction  remain  the 
same,   when   you   divide  botli    numerator   and 
denominator  by  the  same  number  ? 

17.  "When  you  multiply  both  numerator  and  denom- 
inator by  the   same   number,  why  does  it  not 
change  the  value  of  the  fraction  ? 

1 8.  Reduce    4  times  -f%  to  its  lowest  terms. 

19.  Reduce    7  times  T\  to  its  lowest  terms. 

20.  Reduoe    8  times  2J  to  its  lowest  terms. 

21.  Reduce    6  times  •£%  to  its  lowest  terms. 

22.  Reduce    4  times  T5^  to  its  lowest  terms. 

23.  Reduce  12  times  -fg  to  its  lowest  terms. 


COMPOUND      FRACTIONS. 

LESSON     XLI. 

1.  If  you  cut  an  apple  into  2  equal  pieces,  what  part 
of  1  apple  will  1  of  these  pieces  be  called  ? 

2.  If  you  cut  J  of  an  apple  into  two  equal  pieces, 
what  part  of  a  whole  apple  will  1  of  these  pieces 
be  called  ? 

3.  If  Alice  has  J  of  a  lemon,  and  gives  -J  of  it  to  Ann, 
what  part  of  a  lemon  will  Ann  receive  ? 

ANALYSIS. — J  equals  f .     Therefore,  Ann  receives  %  of  f 
of  a  lemon,  which  is  ^  of  a  lemon. 

4.  George,  having  ^  of  a  melon,  gave  -J  of  it  to  Mar- 
cus ;  what  part  of  a  melon  did  Marcus  receive  ? 

5.  Crary  had  \  of  a  dollar,  and  gave  J  of  it  to  Joshua ; 
what  part  of  a  dollar  did  Joshua  receive  ? 

6.  Robert  had  \  of  a  dollar,  and  gave  J  of  it  for  a 
cake ;  how  many  cents  did  the  cake  cost  him  ? 

7.  Margaret  had  -J  of  a  pound  of  candy,  and  Mary 
had  J  as  much  ;  how  much  had  Mary  ? 

8.  Jane  had  \  of  a  pound  of  sugar,  and  Ann  ^  as 
much  ;  how  much  had  Ann  ? 

9.  A  boy  bought  J  of  a  quart  of  chestnuts,  and  gave 
J  of  them  to  his  sister ;  what  part  of  a  quart  did 
she  receive  ? 

10.  A  man  owned  ^  of  a  share  in  a  bank,  and  sold  J 
of  it ;  what  part  of  a  share  had  he  remaining  ? 

11.  B.  owned  -J  of  a  ship,  and  sold  \  of  his  share; 
what  part  of  a  whole  ship  did  he  sell  ? 

12.  What     is     J     of    I  ? 

ANALYSIS  IST.— |  equals  -&-,  £  of  ^  is  T\  ;  therefore, 
i-  °f  1  equals  ^ 
ANALYSIS  3D. — %  °f  i  *s  ^r- 

13.  What     is     -|     of    J-  ? 

14.  What     is     J     of    |? 

15.  What     is     |     of    1? 

1 6.  What    is    J    of    1  ? 

17.  What     is     |     of    i? 


COMPOUND     FRACTIONS.  97 

1 8.  What    is     \    of    J  ? 

19.  What     is     J     of    -J? 

20.  What     is    T\    of    j  ? 

21.  A  kite  up  in  the  air  fell  f  of  its  height,  it  then 
arose  ^  of  its  distance  from  the  ground ;  what  part 
of  the  whole  distance  was  it  above  the  ground  \ 

22.  Homer  is  1  as  old  as  his  father,  and  Nelson  is  ^ 
as  old  as  Homer ;  what  part  of  the  father's  age  is 
Nelson's  age  ? 

23.  A  man,  owning  ij-  of  a  barrel  of  fish,  accommo- 
dated his  neighbor  with  |  of  what  he  owned: 
how  much  had  he  remaining  ? 

24.  A  man,  having  J  of  an  Eagle,  gave  £  of  it  to  B, 
and  B  gave  ^  of  what  he  had  to  C ;  how  many 
cents  had  each  ? 

25.  Elizabeth  had  J  of  a  pie,  and  gave  |  of  her  piece  to 
Harriet ;  how  much  of  the  pie  did  Harriet  receive  ? 

ANALYSIS  IST. — £  of  £  is  £.    If  £  of  £  is  -J-,  ^  of  f  is  twice 
|,  which  are  f .     Therefore,  Harriet  had  f  of  a  pie. 
ANALYSIS  2D. — ^  of  f  is  f . 


26. 

What 

is 

i 

of 

It 

27. 

What 

is 

i 

of 

1? 

28. 

What 

is 

of 

*» 

29. 

What 

is 

I 

of 

i? 

3°- 

What 

is 

^ 

of 

I? 

31- 

What 

is 

4. 

of 

l? 

32. 

What 

is 

I 

of 

33- 

What 

is 

of 

4  ? 

34- 

What 

is 

I 

of 

f! 

35- 

What 

is 

" 

of 

36. 

What 

is 

of 

£> 

37- 

What 

is 

•J 

oC 

38. 

What 

is 

| 

of 

f  . 

39- 

What 

is 

^ 

of 

If? 

40. 

What 

is 

I 

of 

i  ' 

98 


COMPOUND     FRACTIONS. 


41.  What  is  I 

42.  What  is  | 

43.  What  is  | 

44.  What  is  f 

45.  What  is  f 

46.  What  is  | 

47.  What  is  | 

48.  What  is  f 

49.  What  is  | 

50.  What  is  | 

51.  What  is  | 

52.  What  is  | 

53.  What  is  | 

54.  What  is  | 

55.  What  is  f 

56.  What  is  | 

57.  What  is  | 

58.  What  is  | 

59.  What  is  f 

60.  What  is  & 
6  1.  What  part 
62.  What  part 

ANALYSIS  IST.  —  f  of  £  is  f. 
of  |,  which  is  £  of  2. 

ANALYSIS  SD.  —  |  of  £  is  f.     1 
of  £?  or  ^  of  2,  and  f  are  2  times 

64.  What  part  of 

65.  What  part  of 

66.  What  part  of 

67.  What  part  of 

68.  What  part  of 

69.  What  part  of 

70.  What  part  of 


of  i  ? 

of  |  ? 

of  I  'I 

of  $  ? 

of  |? 

of  1? 

of  |? 

of  J? 

of  J  ? 

of  \\ 

of  |? 

of  §  ? 

of  f  f 

of  |  ? 

of  I  ? 

of  f  ? 

of  |  ? 

of  |? 

of  f? 

of  f? 

of  1     is     f     of    J  ? 

of  2     is     f     of    |  ? 

is  f  of  1,  and  is,  therefore,  \ 

is  £  of  2.    If  1  is  |  of  2,  |  is  \ 
T^,  or  £  of  2. 

2  is  J  of  If? 

2  is  f  of  \\ 

3  is  \  of  |  ? 

4  is  |  of  If? 

5  is  \-  of  |1 
9  is  f  of  1£  ? 
2  is  f  of  |? 


COMPOUND      FRACTIONS.  99 


71- 
72. 
73- 
74- 
•75- 
76. 

77- 

What 
What 
What 
What 
What 
What 
Anthony 

part 
part 
part 
part 
part 
part 
had  £ 

of 
of 
of 
of 
of 
of 
of  | 

2 
4 
6 
3 

4 

7 

:  Of 

is 
is 
is 
is 
is 
is 
a 

|     of 
I     of 
f     of 

i    of 
i    of 

1     of 
pound 

2£2 

J|? 
4f  ? 
12$? 
10f? 
of  cinn 

what  part  of  a  pound  had  he  ? 

78.  Albert  had  if-  of  f  of  a  quart  of  strawberries; 
how  many  strawberries  had  he,  provided  1  quart 
contained  42  strawberries  ? 

79.  Abner  gave  ^  of  f  of  a  melon  to  his  brother; 
what  part  of  a  melon  had  he  remaining  ? 

80.  Matilda  bought  |  of  a  quart  of  milk  for  tea,  and 
spilled  J  of  it  ;  what  part  of  a  quart  had  she  re- 
maining ? 

81.  Edwin  picked  J  of  a  pailful  of  blackberries,  and 
on  his  way  home  spilled  ^  of  them  ;    what  part 
of  a  pailful  had  he  remaining  ? 

82.  A  merchant-  bought  •£  of  a  hogshead  of  molasses, 
and  lost  ^  of  it  by  leakage  ;  what  part  of  a  hogs- 
head had  he  remaining  ? 

83.  Miriam  had  f  of  a  pound  of  candy,  and  gave  f  of 
it  to  Augusta  ;  what  part  of  a  pound  did  she  give 
Augusta  ? 

84.  Elisha  found  $f  ,  and  gave  |  of  it  to  Ephraim  ; 
what  part  of  a  dollar  had  Elisha  remaining  ? 

85.  Andrew  bought   f  of  a  pound  of  maple-sugar, 
and  gave  f  of  it  to  Walter;  what  part  of  a  pound 
did-  Walter  receive  ? 

86.  Jacob,  having  a  pine-apple,  gave  f  of  f  of  it  to 
the  one  that  could  tell  how  much  that  would  be  ; 
\rhat  part  of  it  had  Jacob  remaining  ? 

87.  James  gave  f  of  f  of  a  dime  for  a  top  ;  how  many 
cents  did  the  top  cost  him  ? 

88.  Robert  gave  |  of  a  dollar  for  a  cap  ;  how  many 
cents  did  the  cap  cost  him  ? 


100  SIMPLE     PROPORTION. 

89.  Mary  gave  J-  of  If  dimes  for  a  comb ;  how  many 
cents  did  the  comb  cost  her  ? 

90.  Clarinda  gave  f  of  6  dimes  for  a  pair  of  gloves  ; 
how  many  cents  did  the  gloves  cost  I 

91.  A  man,  having  4f  barrels  of  flour,  sold  f  of  it ; 
how  much  remained  unsold  ? 

92.  A  man  gave  f  of  $3-J  for  a  silver  pencil ;   what, 
was  the  cost  of  the  pencil  ? 

93.  Jane  worked  8|  hours  in  a  day,   and   Delilah 
worked  only  |  of  as  many  ;    how  many  hours  in 
a  day  did  Delilah  work  ? 

94.  B.  gave  $32|  for  a  cow,  which  was  §  as  much  as 
A.  gave  for  his ;   how  much  more  did  A.'s  cow 
cost  than  B.'s  ? 

95.  Darius  is  18|  years  old,  which  is  f  of  Daniel's 
age ;  how  old  is  Daniel  ? 

96.  If  1  yd.  of  cloth  cost  $5|,  what  will  f  yd.  cost  ? 

97.  If  4  yd.  of  cloth  cost  $94-,  what  will  f  yd.  cost  ? 

98.  If  5  bbl.  of  beet  cost  $18£,  what  will  |  bbl.  cost? 

99.  If  |  of  an  apple  cost  f  of  a  cent,  what  will  1 
apple  cost  ? 

100.  If  \  of  an  orange  cost  1J  cents,  what  will  -f$  of 
an  orange  cost  ? 

io*.  If  4  pounds  of  rice  cost  6J  dimes,  how  many 
cents  will  If  pounds  cost  ? 


LESSON     X  L 1 1 . 

1 .  If  4  bbl.  ci  flour  cost  $14|,  what  will  f  of  a  bbl.  costt 

2.  If  3  bu.  of  pears  cost  $5|,  what  will  1^-  bti.  cost  ? 

3.  If  2^  bushels  of  apples  cost  6J  dimes,  how  many 
cents  will  |  of  a  bushel  cost  ? 

4.  If  |  of  an  apple  cost  f  of  a  cent,  what  will  1  apple 
cost  ? 

5.  If  §  of  an  orange  cost  f  of  a  cent,  what  will  f  of 
an  orange  cost? 


DIVISION     OF     FRACTIONS. 


101 


6.  If  2f  yd.  of  silk  cost  $3f,  what  will  5  J  yd.  cost  ? 

7.  If  5f  yd.  of  satin  cost  $5-^-,  what  will  2  yd.  cost  ? 

8.  If  in  3^  hours,  A.  can  do  a  piece  of  work,  how  long 
will  it  take  him  to  do  a  piece  If  times  as  large  ? 

9.  f  of  A.'s  age  is  J  of  B.'s ;  and  f  of  B.?s  age  is  f  of 
C.'s  age.     How  old  are  A.  and  B.  respectively, 
provided  C.  is  81  years  old  ? 

JO.  Bought  3f  boxes  of  goods,  at  $6-3^  a  box;  how 
many  sheep,  at  $2  each,  will  pay  for  them  '$ 

NOTE. — The  expression,  =  ?,  is  read,  equals  how  many. 

11.  7-i-f =  ?     Or,  7  divided  by  f  equals  how  many  ? 

ANALYSIS. — f  is  contained  in  1,  f  times,  and  in  7,  7  times 
|,  which  are  -?/,  or  17£  times. 

12.  2  — J  =  ?  15.        6-f  =  2 

13.  3  — f  =  ?  16.       9--?-  =  ? 

14.  5  — -f  =  ?  17.     12  —  $  =  ?      . 

1 8.  How  many  times  f  is  f  ? 

ANALYSIS  1st. — f  equals  ^,  and  f  equals  £-&.  ^  fa 
contained  in  ££,  -1/,  or  1£  times. 

ANALYSIS  2D. — 1  is  contained  in  f ,  f  times.  If  1  is  con- 
tained in  f ,  |  times,  i  is  contained  in  ^f,  5  times  f  times, 
which  are  -^  times,  and  f  is  contained  in  it,  ^  of  -lf5-  times, 
which  is  J  or  1  times. 


19- 

Ho^ 

r     mai 

20. 

I-   ' 

-!  = 

21. 

f    ~ 

-!  = 

22. 

A- 

-I  = 

23' 

H  ~ 

-1  = 

24. 

A- 

-    7    = 

2 

-5* 

g-    - 

26. 

3f  - 

-  i  — 

27. 

8- 

-i  = 

f5    

times     |     is     j  ? 


29. 

31- 
32- 
33- 
34- 
35- 
36. 
37- 


A 
« 


-   I   =» 


i 
H 


-  31-  =! 


102  DIVISION     OF     FRACTION  S. 

38.  A  farmer  sold  a  quantity  of  rye  for  $96,  which 
was  only  -|  of  its  value ;  how  much  did  he  lose  ? 

39.  A  man  sold  a  cow  for  1  f  times  what  she  cost 
him,  and  by  so  doing  gained  $6  ;  how  much  did 
the  cow  cost  him  ? 

40.  A  merchant  sold  a  quantity  of  goods  for  ||  of 
what  they  cost  him,  and  by  so  doing  lost  $15  ; 
how  much  did  the  goods  cost  \ 

41.  A  farmer,  having  lost  12  sheep,  had  only -J  of  his 
flock  remaining  ;  how  many  sheep  had  he  left  ? 

42.  An  individual  being  asked  how  many  geese  he 
had,  answered,  if  to  \  of  his  flock  24  geese  were 
added,  the   number   would   equal  If  times  his 
original  flock  ;  how  many  geese  had  he  ? 

43.  If  f  of  a  yard  of  cloth  cost  $j,  what  will  f  of  a 
yard  cost  ? 

44.  A  boy,  being  asked  his  age,  said,  that  8J  years 
equaled  |  of  twice  his  age  ;  how  old  was  he  ? 

45.  If  -p-  of  my  steamboat  fare  was  $>7J,  what  was  | 
of  it? 

46.  What  will  f  of  a  barrel  of  flour  cost,  if  f  of  a 
barrel  cost  $2f  ? 

47.  What  will  §  of  an  orange  cost,  if  |-  of  an  orange 
cost  2£  cents  ? 

48.  How  many  yards  of  cloth  will   be   required  to 
make  a  coat,  if  1|  yards  will  make  f  of  a  coat  ? 

49.  f  of  2  are  how  many  times  |  ? 

50.  -^Q  of  8  are  how  many  times  J  ? 


52. 


-H  x  7- 


53- 

54. 


55.  If  |  of  3  yards  of  cloth  cost  $1|,  what  will  |  of 
7  yards  cost  ? 

56.  If  f  of  6  yards  of  cloth  cost  §2f  ,  how  much  will 
|  of  7  yards  cost  ? 

57.  If  f  of  f  of  a  barrel  of  flour  cost  $1|,  what  will 
J  of  f  of  |  of  a  barrel  cost  I 


FRACTIONS.  103 

WESSON     XLIII. 

r .         12    is     I     of    what     number  ? 

ANALYSIS. — If  f  of  some  number  is  12,  £  of  that  number  is  £ 
of  12,  or  4 ;  and  £,  which  is  that  number,  are  4  times  4,  which 
are  16.  Therefore,  12  is  £  of  16. 

2.  15  is  |  of  what  number? 

3.  18  is  f  of  what  number? 

4.  20  is  |  of  what  number? 

5.  26  is  |  of  what  number? 

6.  25  is  f  of  what  number? 

7.  30  is  |  of  what  number? 

8.  32  is  f  of  what  number? 

9.  36  is  f  of  what  number? 

10.  36     is    i6T    °f    what     number? 

11.  36     is     |     of    what     number? 

12.  24     is     f     of    what     number? 

13.  9     is     f     of    what     number? 

14.  12  is  |  of  what  number? 

15.  38  is  |  of  what  number? 

1 6.  16  is  f-  of  what  number? 

17.  16  is  -f-  of  what  number? 

1 8.  16  is  f  of  what  number? 

19.  40  is'  f  of  what  number? 

20.  40  is  |  of  what  number? 
ANALYSIS. — 40  is  -f  of  45. 

REMARK. — When  pupils  are  familiar  with  the  analysis  of 
these  questions,  the  intermediate  steps  may  be  omitted,  as  in 
the  above  analysis. 

21.  72  id    •$  of  what    number  ? 

22.  72  is   •£$  of  what    number? 

23.  12  is     f  of  how  many  times    2? 

24.  16  is     -J  of  how  many  times    3  ? 

25.  18  is     f  of  how  many  times     9  ? 


1 04  FRACTIONS. 


26.  32  is  |   of  how  many  times  4  ? 

27.  46  is  f  of  how  many  times  23  ? 

28.  48  is  |  of  how  many  times  5  ? 

29.  48  is  f  of  how  many  times  4  ? 

30.  36  is  f  of  how  many  times  2  ? 

31.  30  is  f  of  how  many  times  \  of  12  ? 

32.  30  is  f  of  how  many  times  ^  of  10  ? 

33.  16  is  |  of  how  many  times  f  of  9  ? 

34.  16  is  T45  of  how  many  times  f  of  16  ? 

35.  24  is  |  of  how  many  times  §  of  12  ? 

36.  25  is  |  of  how  many  times  J  of  9 1 

37.  35  is  T%  of  how  many  times  |  of  9  ? 

38.  40  is  f  of  how  many  times  f  of  10  ? 

39.  48  is  T%  of  how  many  times  -f  of  25  ? 

40.  96  is   |  of  how  many  times  f  of  16  ? 

LESSON     XLIY. 

1.  f  of    6  is   |  of  what  number  ? 

2.  |  of  10  is  |  of  what  number  ? 

3.  |  of    8  is  f  of  what  number  ? 

4.  f  of  21  is  |  of  what  number  ? 

5.  £  of  15  is  ^  of  what  number? 

6.  -^j-  of  40  is  -£  of  what  number  ? 

7.  |  of  27  is  |  of  what  number? 

8.  -§  of  27  is  T%  of  what  number  ? 

9.  |  of  81  is  -fa  of  what  number'? 
10.  f  of  49  is  ^j  of  what  number? 

Ji.  f  of  12  is  |-  of  how  many  times  2  ? 

12.  |  of  16  is  f  of  how  many  times  2  ? 

13.  f  of  10  is  f  of  how  many  times  4? 

14.  i  of  16  is  -j\  of  how  many  times  6  ? 


FRACTIONS.  105 

15.  £  of  15  is   f  of  how  many  times  6? 

1 6.  f  of  20  is   §   of  how  many  times  3? 

17.  |  of  12  is  |  of  how  many  times  5  ? 

1 8.  f  of  20  is  |  of  how  many  times  3  ? 

19.  J  of  36  is  f^  of  how  many  times  4  ? 

20.  |  of  72  is  §  of  how  many  times  12? 
SOLUTION.  — |  of  72  is  64.     64  is  f  of  96.     96  is  8  times  12, 

21.  |  of  90  is  f  of  how  many  times  90  'I 

22.  J  of  117  is  J  of  how  many  times  4? 

23.  |  of  56  is   |  of  how  many  times  8  ? 

24.  |  of  60  is  f  of  how  many  times  5  ? 

25.  f  of  36  is   |  of  how  many  times  12  ? 

26.  I  of  72  is   |  of  how  many  times  5  ? 

27.  |  of  40  is  T5^  of  how  many  times  21  ? 

28.  |  of  32  is  ^  of  how  many  times  9  ? 

29.  |  of  15  is  f  of  how  many  times  2  ? 

30.  I  of  15  is  j-  of  how  many  times  9  ? 

31.  |  of  24  is  |   of  how  many  times  3  ? 

32.  J  of  45  is   |  of  how  many  times  3  ? 

33.  f  of  14  is  f  of  how  many  times  5  ? 

34.  |  of  18  is  |  of  how  many  times  7  ? 

35.  T9^  of  40  is  f  of  how  many  times  6  ? 

36.  ^  of  45  is  -fi  of  how  many  times  3  ? 

37.  |  of  35  is  f  of  how  many  times  2  ? 

38.  |  of  81  is  |  of  how  many  times  9  ? 

39.  |  of    5  is  f  of  how  many  times  7  2 

40.  |  of    7  is  |  of  how  many  times  3  ? 

41.  B.'s  horse  cost  $60,  and  f  of  the  cost  o>   the 
horse  is*  \  of  2  times  the  value  of  his  wagon ; 
what  is  the  value  of  his  wagon  ? 

42.  A  coat  cost  $20,  and  |  of  the  cost  of  the  coat  is 
f  of  8  times  the  price  of  a  hat ;   the  price  of  the 
hat  is  required. 


106  FRACTIONS. 

43.  If  a  cow  cost  $30,  and  f  of  this  is  f  of  10  times 
the  price  of  a  sheep,  what  is  the  price  of  a  sheep '( 

44.  A.'s  farm  is  worth  $1200,  and  £  of  its  value  is  f 
of  10  times  the  value  of  its  yearly  productions ; 
what  is  the  value  of  the  yearly  productions  ? 

45.  The  articles    contained  in  a  certain   store   cost 
$500,  and  y30-  of  their  cost  is  f  of  3  times  the 
amount  paid  for  the  silks  ;  how  much  was  the  cost 
of  the  silks  and  of  the  other  articles  respectively  ? 

46.  A.'s  wedding  clothes  cost  $180,  and  f  of  the  cost  of 
his  clothes  is  |  of  6  times  the  cost  of  his  bride's  wed- 
ding dress  ;  how  much  was  the  cost  of  her  dress  ? 

47.  The  insurance  of  a  ship  amounted  to  $800,  and  \ 
of  that  is  2*5-  of  2  times  the  value  of  the  cargo ; 
what  is  the  value  of  the  cargo  ? 

48.  A.'s  house  cost  $1400,  and  J  of  its  cost  is  3J  times 
|-  of  the  cost  of  the  furniture  contained  in  it ; 
what  was  the  cost  of  the  furniture  ? 

49.  Provided  a  house  was  worth  $1200,  and  f  of  its 
value  was  f  of  \  times  the  value  of  the  farm  on 
which  it  stood ;  what  was  the  value  of  the  farm  ? 

50.  If  a  sleigh  cost  $100,  what  would  be  the  cost  of 
a  wagon,  if  f  of  the  cost  of  the  sleigh  was  -f^  of 
twice  the  cost  of  a  wagon  ? 

51.  Before  the  war   Lambert's   property  was  worth 
$2500,  and  f  of  its  value  then  is  3^  times  \  of  its 
value  after  the  war  ;  what  was  its  last  value  ? 

Distances  on  the  Railroad  between  Albany  and  Buffalo. 

52.  The  distance  from  Albany  to  Schenectady  is  16 
miles,  and  f  of  this  distance  is  f  of  \  of  the 
distance  from  Albany  to  Rome ;  what  is  the  dis- 
tance to  Rome  ? 

53.  Fort-Plain  is  56  miles  from  Albany,  and  f-  of  this 
distance  is  If  times  -^  of  the  distance  from  Albany 
to  Rochester ;  what  is  the  distance  to  Rochester  ? 

54.  Waterloo  is  192  miles  from  Albany,  and  |-  of  this 


FRACTIONS.  107 

distance  is  If  times  the  distance  from  Albany  to 
Utica,  and  3  miles  more ;  what  is  the  distance  to 
Utica?  ' 

55.  Buffalo  is  325  miles  from  Albany,  and  f  of  this 
distance  is  7J  times  -^  of  the  distance  to  Batavia, 
and  5  miles  more  ;    what  is  the  distance  from 
Albany  to  Batavia  ? 

Distances  on  the  Railroad  between  Albany  and  Boston, 

56.  Boston  is  200  miles  from  Albany,  and  f  of  this 
distance  is  1-f  times  -J  of  the  distance  to  West 
Springfield ;  what  is  the  distance  to  West  Spring- 
field ? 

57.  From  Albany  to  the  State  line  is  38  miles,  and  1^ 
times  this  distance  is  4f  times  ^  of  the  distance  to 
Wilbraharn  ;  what  is  the  distance  to  Wilbraham  ? 

58.  Kinderhook  is  16  miles  from  Albany,  and  I  of 
this  distance  is  f  times  J  of  the  distance  to  Dai- 
ton  ;  what  is  the  distance  to  Dalton  ? 

59.  Brighton  is  195  miles  from  Albany,  and  f  of  this 
distance  is  J  of  2  times  the  distance  to  Worcester ; 
what  is  the  distance  to  Worcester  ? 

60.  Graft  on  is  162  miles  from  Albany,  and  |  of  this 
distance  is  J  of  3  times  the  distance  to  Westfield, 
less  2  miles ;  how  far  is  it  to  Westfield  ? 


LESSON     XLY. 

1.  §  of    9  is  |  of  how  many  times  -J  of  25  ? 

2.  |  of  16  is  \  of  how  many  times  j  of  21  ? 

3.  |  of  40  is  |  of  how  many  times  ^  of  16  ? 

4.  -|  of  80  is  |  of  how  many  times  J  of  21  ? 

5.  f  of  36  is  \  of  how  many  times  j  of  12  ? 

6.  |  of  45  is  f  of  how  many  times  f  of  14  ? 

7.  I   of  30  is  |  of  how  many  times  J  of  10  ? 

8.  \\  of  48  is  \  of  how  many  times  f  of  7  ? 


108  FRACTIONS. 


9.  |  of  35  is  |  of  how  many  times  f  of  8  ? 

ANALYSIS.— f  of  45  is  36.     36  is  f  of  162.     f  of  8  i: 
162  is  27  times' 6. 

10.  f  of  35  is  £  of  how  many  times  f  of  llf  ? 
u.  |  of  54  is  f  of  how  many  times  |  of  lo|? 
J2.  |  of  25  is  I  of  how  many  times  f  of  10  ? 

13.  -f  of  28  is  §  of  how  many  times  $  of  25  ? 

14.  -|  of  18  is  f  of  how  many  times  f  of  12  ? 

15.  |  of  36  is  jj  of  how  many  times  |  of  12  ? 

1 6.  |  of  54  is  |  of  how  many  times  |  of  16  ? 

17.  |  of  32  is  |  of  how  many  times  f  of  9  ? 

1 8.  I  of  108  is  §  of  how  many  times  j  of  f  of  15  ? 

19.  |  of  40  is  -f%  of  how  many  times  J  of  f  of  20  ? 

20.  |  of  20  is  |  of  how  many  times  |  of  |  of  12  ? 


LESSON     X  L  V I . 

1.  If  1  horse  eat  J  of  a  bushel  of  oats  in  1  day,  how 
many  horses  will  eat  a  bushel  in  the  same  time  ? 

2.  If  the  wages  of  8  weeks  amount  to  $48,  what  will 
the  wages  of  2|  weeks  amount  to  ? 

3.  A  ship's  crew  of  12  men   have  provision  for  5 
months ;  how  many  months  will  if  last  5  men  ? 

4.  A  man  gained  $14  by  selling  a  watch  for  1 f  times 
what  it  cost  him ;  how  much  did  it  cost  ? 

5.  There  is  a  pole,  1  of  its  length  is  under  water,  and 
9  feet  out ;  how  long  is  the  pole  ? 

6.  A  pole  is  standing  in  the  water,  so  that  15  feet  is 
above  the  water,  which  is  f  of  the  whole  length  of 
the  pole  ;  how  long  is  the  pole  ? 

7.  If  |  be  2,  what  will  2  be «     Or,  if  f  of  an  apple 
cost  2  cents,  how  much  will  2  apples  cost  ? 

8.  If  8  horses  in  1  day  eat  4  bushels  of  oats,  in  how 
many  days  can  1  horse  eat  1  bushel  ? 


COMPOUND     FBOPORTION.  109 

9.  If  3  horses  in  1  day  eat  If  bushels  of  oats,  how 
many  bushels  can  1  horse  eat  in  4  days  ? 

10.  If  1  horse  in  2  days  eat  6  bushels  of  corn,  how 
many  bushels  will  4  horses  eat  in  3  days  ? 

1 1.  If  4  horses  eat  16  bushels  of  grain  in  2  days,  how 
many  bushels  will  3  horses  eat  in  12  days  ? 

1 2.  How  many  tons  of  hay  will  3  horses  consume  in  4 
days,  if  4  horses  in  J  of  a  day  consume  -f  of  a  ton  ? 

13.  How  many  hundred- weight  of  hay  can  3  horses 
consume  in  25  days,  if  2~ horses  in  \  of  a  day  con- 
sume 3  J-g-  of  a  hundred- weight  ? 

14.  In  how  many  days  can  4  men   cut  16  cords  of 
wood,  if  1  man  in  1  day  cut  ^  of  a  cord  ? 

15.  How  many  men  will  be  required  to  earn  20  dimes 
in  4  days,  if  4  men  in  2J  days  earn  11  dimes  ? 

1 6.  If  it  require  6  days  for  2  men  to  lay  36  rods  of 
wall,  how  many  men  can  in  J  of  the  time  build 
72  rods  of  similar  wall  ? 

17.  If  in  4  days  3. men  accomplish  a  certain  piece  of 
work,  how  many  men  will  be  required  to  perform 
a  piece  of  work  4  times  as  large  in  2  days  ? 

1 8.  If  4  men  in  8  days  perform  a  certain  piece  of 
work,  how  many  men  will  be  required  to  accom- 
plish 3  times  as  much  work  in  f  of  a  day  ? 

19.  If  1  horse  eat  1  bushel  of  oats  in* 4  days,  in  how 
many  days  would  6  horses  eat  48  bushels  ? 

20.  If  j  "of  6  be  3,  what  will  }  of  40  be  ? 

21.  If  3  be  |  of  6,  what  will  \  of  40  be  ? 

22.  If  2  men  in  J  of  a  day  earn  -f$  of  a  dollar,  in  how 
many  days  can  3  men  earn  f  of  a  dollar  ? 

23.  If  it  require  -J-  of  a  bushel  of  oats  to  feed  4  horses 
J  of  a  day,  how  many  horses  would  it  require  to 
consume  9  bushels  in  f  of  a  day  ? 

I2F"  SUGGESTION. — Review  unless  the  pupils  thoroughly  under- 
stand the  preceding  Lessons. 

The  study  of  the  following  "Arithmetical  and  Algebraic 
Problems"  may  be  omitted  until  the  class  has  learned  the 
Lessons  in  Interest,  commencing  on  page  141. 


110  QUESTIONS. 

LESSON     XLYII. 
ARITHMETICAL  AND  ALGEBRAIC   PROBLEMS. 

1.  24  is  f  of  twice  as  much  as  a  cask  of  wine  cost ; 
what  did  the  wine  cost  ? 

2.  Bought  30  barrels  of  flour,  and  -J  of  the  number 
of  barrels  equaled  -J  as  many  dollars  as  they  all 
cost ;.  what  did  1  barrel  cost  ri 

3.  35  is  f  of  how  many  times  f  of  4  ? 

4.  A  farmer,  being  asked  how  many  sheep  he  had, 
answered,  that  160  was  f  of  10  times  his  number ; 
how  many  sheep  had  he  ? 

5.  MrT  B.,  being  asked  the  value  of  his  horse,  said, 
$54  is  T6T  of  3  times  its  value ;  what  is  the  value 
of  his  horse  ? 

6.  72  is  |  of  how  many  times  f  of  12  ? 

7.  36  is  |  of  how  many  times  §  of  12  ? 

8.  43  is  §  of  how  many  times  J  of  18  ? 

9.  56  is  |  of  how  many  times  -|  of  8  ? 
10.  60  is  |  of  how  many  times  |  of  16  ? 
ir.  84  is  ^  of  how  many  times  £  of  25  ? 

12.  A.  spent  $60,  which  was  f  of  4  times  as  much  as 
he  was  worth ;  how  much  was  he  worth  ? 

13.  B.  sold   9  sheep,  which  was  -f$  times  ^  of  his 
whole  flock ;  how  many  sheep  had  he  remaining  ? 

14.  D.,  at  a  game  of  cards,  lost  $20,  which  was  $ 
times  f  of  all  his  money ;  how  much  had  he  ? 

15.  C.  found  $45,  which  was  |  of  3  times  as  much  as 
he  already  had  ;  how  much  more  did  he  find  than 
he  had  at  first  ? 

1 6.  A  boy  lost  9  marbles,  which  was   |  of  twice  the 
number  he  had  at  first ;  how  many  had  he  left '{ 

17.  A  boy  gave  away  8  apples,  which  was  f  of  twi,-- 
as  many  as  he  had  left ;  how  many  had  he  at  fir*t  -: 


QUESTIONS.  Ill 

1 8.  12  is  |  times  f  of  what  number  ? 

19.  36  is  T\-  times  f  of  how  many  times  f  of  13  J  ? 

20.  Jeremiah  is  18  years  old,  and  his  age  is  j  times 
f  of  his  father's  age ;  how  old  is  his  father  ? 

2 1 .  Mary  gave  6  cents  for  a  comb,  which  was  f  times 
J  of  all  her  money ;  how  many  cents  had  she  '( 

22.  Martha  gave  8  cents  for  a  pine-apple,  which  was 
f-  times  \  of  all  her  money ;   how  many  apples 
could  she  have  bought  with  the  money  she  had 
remaining,  at  2  cents  each  ? 

23.  Henry  had  20  marbles,  which  was  §  of  twice  as 
many  as  Harry  had;  ho\v  many  had  Harry? 

24.  Margaret  is  16  years  old,  and  her  age  is  f  of  3 
times  Martha's  age  ;  how  old  is  Martha  ? 

25.  f  is  f  of  twice  as  much  as  what  number  ? 

26.  A  man  bought  a  horse  for  $60,  which  was  f  of 
twice  as  much  as  he  sold  it  for ;  how  much  did 
he  gain  by  the  bargain  ? 

27.  A  horse  was  sold  for  $40,  which  was  |  times  | 
of  what  it  was  worth ;  what  was  the  value  of  the 
horse  ? 

28.  A  man  when  he  was  married,  was  20  years  of  age, 
which  was  f  times  f  of  the  age  of  his  wife ;  how 
old  was  she  ? 

29.  Shepherd  was  worth  $160,  which  was  f  times  -^ 
of  his   father's   fortune ;     required   the   father's 
fortune. 

30.  A.  and  B.  were  playing  cards,  B.  lost  $14,  which 
was  -fa  times  f  as  much  as  A.  then  had  ;    and 
when  they  commenced,  f  of  A.'s  money  equaled 
f  of  B.'s.    How  much  had  each  when  they  began 
to  play  ? 

3 1 .  A.  and  B.  were  playing  cards,  A.  lost  $20,  which 
was  A  of  the  number  of  dollars  B.  then  had 
more  than  A. ;   provided  this  sum  was  1 J  times 
as  much  as  A.  had  at  first,  how  much  had  each 
when  they  began  to  play  \ 


112  QUESTION 


LESSON     XLVIII. 

1 .  A  boy,  after  spending  f  of  all  his  money,  found 
that  16  cents  was  all  be  had  remaining;    how 
much  had  he  at  first  ? 

ANALYSIS  IST. —  Let  %  equal  the  money  he  had  at  first. 
Then,  after  spending  f  of  it,  he  had  remaining  f— f,  which 
is  f.  This,  by  the  condition  of  the  question,  is  16  cents. 
If  f  of  the  money  he  had  at  first  is  16  cents,  -£•  of  it  is  4  of 
16  cents,  which  is  8  cents  ;  and  f,  or  what  he  had  at  first, 
are  5  times  8,  or  40  cents. 

ANALYSIS  2n. —  He  spent  f  of  his  money;  therefore,  he 
had  remaining  f  of  it,  which  equals  16  cents.  If  f  of  his 
money  is  16  cents,  he  must  have  had  40  cents. 

2.  Ruth,  after  losing  f  of  all  her  roses,  had  only  3 
remaining ;  how  many  had  she  at  first  ? 

3.  Jane  gave  f  of  all  her  flowers  to  Ann,  and  had  4 
remaining ;  how  many  did  she  give  to  Ann  ? 

4.  George,  after  eating  T9^  of  all  his  oranges,  had  only 
8  oranges  remaining ;  how  many  had  he  at  first  ? 

5.  A  boy  expended  |  of  his  money  for  a  pie,  |  for  a 
ball,  ^  for  a  top,  and  had  6  cents  remaining ;  how 
many  cents  had  he  at  first  ? 

6.  In  a  certain  school  \  of  the  scholars  study  gram- 
mar, J  study  arithmetic,  and  the  remainder,  which 
is  10,  study  geography;  how  many  scholars  in  all, 
arid  how  many  attending  to  each  study  ? 

7.  A  third  part  of  an  army  was  killed,  \  part  taken 
prisoners,  and  300  escaped ;  how  many  were  there 
in  the  army '( 

8.  If  from  my  age  you  subtract  \  and  f  of  my  age, 
the  remainder  is  2  years ;  how  old  am  I  ? 

9.  Mr.  B.,  being  asked  how  many  pigeons  he  caught, 
said,  that  if  to  f  of  the  number  36  were  added,  the 
sum  would  equal  twice  the  number;   how  many 
did  he  catch  ? 


QUESTIONS.  113' 

10.  If  to  f  of  the  cost  of  B.'s  horse  you  add  $100,  the 
sum  will  be  twice  the  cost  of  the  horse ;  what 
was  the  cost  of  the  horse  ? 

1 1 .  A  gentleman,  after  spending  f  of  his  fortune  and 
£  of  the  remainder,  had  $2400  remaining ;  what 
was  his  fortune  ? 

12.  A  gambler  lost  |  of  all  his  money,  and  the  next 
night  he  won  f  as  much  as  he  lost  the  night  be- 
fore ;   he  then  had  $90.     How  much  had  he  at 
first? 

1 3.  John  had  stolen  from  him  f  of  his  money ;  the 
thief  was  not  caught  until  he  had  spent  f-  of  all 
he  had  stolen  ;  the  remainder,  which  was  $40  less 
than  John  had  remaining,  was  given  back ;  how 
much  money  had  John  at  first  \ 

1 4.  A  traveler  had  stolen  from  him  \-  of  his  money ; 
the  thief  was  not  caught  until  he  had  spent  \  of 
what  he  had  stolen  ;   the  remainder,  $100,  was 
given  back ;  how  much  had  he  at  first  ? 

15.  If  to  \  of  the  cost  of  A.'s  watch  you  add  $10,  the 
sum  will  be  $21 ;  what  was  the  cost  of  his  watch  ? 

1 6.  If  to  f  of  B.'s  age,  you  add  15  years,  the  sum 
would  be  39  years  ;  how  old  is  B.  \ 

17.  A  drover,  being  asked  how  many  sheep  he  had, 
said,  if  to  \  o%my  flock  you  add  the  number  9^, 
the  sum  will  be  99 J;  how  many  sheep  had  he  2 

1 8.  ^  of  the  length  of  a  pole  is  in  the  water,  and  12 
feet  in  the  air ;  how  long  is  the  pole  ? 

19.  If  to  |  of  A.'s  age  you  add  16  years,  the  sum  will 
be  1  \  times  his  age  ;  how  old  is  he  ? 

20.  A   man,    being    asked    how   many   pigeons   he 
caught,  replied,  if  to  f  of  the  number  I  caught 
you  add  20,  the  sum  would  lack  4  of  being  equal 
to  1 J  times  the  number ;  how  many  did  he  catch  ? 


114  PARTNERSHIP. 

LESSON     XLIX. 

1.  Divide  the  number  36  into  two  parts,  which  shall 
be  to  each  other  as  7  to  2. 

ANALYSIS. — Since  the  two  parts  are  to  be  to  each  other  as 
7  to  2,  we  must  divide  36  into  7  +  2,  which  are  9  equal  parts ; 
and  7  of  the  parts  will  be  one  of  the  numbers,  and  2  of  them 
the  other.  -£-  of  36  is  4,  and  -|  are  7  times  4,  which  are  28 
(the  first  number),  and  f  are  2  times  4,  which  are  8  (the  other 
number).  Or,  in  the  latter  part  of  the  solution,  say :  %  of  36 
is  28,  the  first  number ;  and  f  of  36  is  8,  the  other  number. 

2.  2  men  hired  a  pasture  for  $72  ;  one  put  in  7  horses, 
and  the  other  2  horses ;  what  ought  each  to  pay  ? 

3.  A.  and  B.  hired  a  pasture  for  $14 ;  A.  put  in  4  cows, 
and  B.  put  in  3  cows ;  what  ought  each  to  pay  ? 

4.  A.  and  B.  bought  a  lottery  ticket  for  $5  ;   A.  paid 
$3,  and  B.  paid  $2.     They  drew  a  prize  for  $60 ; 
what  was  each  one's  share  ? 

5.  Two  men  bought  40  mules :  the  first  paid  $5  as 
often  as  the  other  paid  $3.     How  many  mules 
ought  each  to  receive  ? 

6.  Mary  and  Elizabeth  went  to  school  80  days,  and 
as  often  as  Mary  went  3  days,  Elizabeth  went  5 
days ;  how  many  days  did  each  attend  school  ? 

7.  Keuben  had  7  cents,  and  Blake  4  cents ;  they  paid 
all  their  money  for  22  apples ;  how  many  apples 
ought  each  to  receive  ? 

8.  Three  men  bought  a  lottery  ticket  for  $12 ;  the 
first  paid  $2,  the  second  $7,  and  the  third  $3.    They 
drew  a  prize  of  $240 ;  what  was  each  man's  share  \ 

9.  Three  men  hired  a  pasture  for  $24  ;  the  first  put  in 
2  horses,  the  second  put  in  3  horses,  and  the  third 
put  in  4  horses  ;  how  much  ought  each  to  pay  ? 

i  o.  A  man,  failing  in  business,  was  able  to  pay  only 
f  of  his  debts ;  how  much  will  that  man  receive  to 
whom  he  owes  $90  ? 

1 1 .  A  man,  meeting  an  equal  number  of  poor  women 
and  boys,  gave  to  each  woman  7  dimes,  and  to  each 


PARTNERSHIP.  115 

boy  2  dimes  :  and  to  them  all  he  gave  $9 ;  how 
many  women  and  boys  were  there  respectively? 

1 2.  Two  men  bought  a  barrel  of  fish  for  $9  ;  the  first 
paid  $4,  the  second  $5 ;  what  part  of  the  barrel 
belongs  to  each  ? 

13.  A  firmer  gave  35  bushels  of  rye  to  two  neighbors ; 
to  the  first  he  gave  1  bushel  as  often  as  to  the  other 
I  of  a  bushel ;  how  many  bushels  did  each  receive  ? 

14.  Three  men  hired  a  pasture  for  $36  :  the  first  put 
in  3  horses,  the  second  2  horses,  and  the  third  4 
horses ;  how  much  ought  each  to  pay '( 

15.  Two  men  hired  a  pasture  for  $60 :  the  first  put 
in  4  horses  for  2  weeks,  and  the  second  put  in  3 
horses  for  4  weeks  ;  how  much  ought  each  to  pay  ? 

1 6.  Three  men  hired  a  pasture  for  $15  :  the  first  put 
in  4  sheep  for  5  weeks,  the  second  put  in  8  sheep 
for  5  weeks,  and  the  third  put  in  10  sheep  for  9 
weeks.     How  much  ought  each  to  pay? 

17.  Two  men  entered  into  partnership;  the  first  put 
in  $  U)  for  10  months,  and  the  second  put  in  $80 
for  5  months ;  they  gained  $95  :   what  was  each 
man's  share  of  the  gain  ? 

1 8.  A.  and  B.  agreed  to  cut  a  field  of  wheat  for  $20  ; 
A.  sent  5  men  for  4  days,  and  B.  sent  3  men  for 
10  days  :  how  much  ought  each  to  receive  ? 

19.  Divide  $56  between  A.  and  B.,  giving  to  A.  $1 
as  often  as  to  B.  f  of  a  dollar. 

20.  A.  and  B.  hired  a  pasture  for  $24 ;  A.  put  in  4 
sheep  for  10  weeks,  and  B.  put  in  2  horses  for  10 
weeks ;  what  ought  each  to  pay,  provided  2  sheep  in 
1  week  eat  as  much  as  a  horse  in  the  same  time? 

21.  Simpson,  Domer,  and  Eyer  enter  into  a  joint 
speculation  by  which  they  clear  $460.     Simpson 
claims  to  have  furnished  \ ;  Domer,  | ;  and  Eyer, 
J  of  the  entire  capital.     How  much,  according  to 
these  calculations,  ought  each  to  receive  ? 

NOTE. — f,  f,  and  £  are  to  each  other  as  9.  8,  and  6. 


116  ALGEBRAIC     QUESTIONS. 


LESSON     L. 

1.  Mr.  B.  had  4  apples  more  than  A.,  and  together 
they  had  14 ;  how  many  had  each  ? 

ANALYSIS. — By  a  condition  of  the  question,  B.'s  number 
is  equal  to  A.'s +  4  apples ;  to  which  add  A.'s  number,  and 
•we  have  2  times  A.'s  number-f  4— 14.  Therefore,  2  times 
A.'s  number  equals  14—4,  or  10  ;  and  once  his  number 
equals  |  of  10,  or  5  apples.  And  B.'s  number  is  5  +  14=9 
apples. 

2.  Hemaa  has  6  books  more  than  Handford,  and 
both  have  26  ;  how  many  has  each  ? 

3.  Robert  has  7  marbles  more  than  Richard,  and 
both  have  35 ;.  how  many  has  each  ? 

4.  Mary  has  4  roses  more  than  Martha,  and  both 
have  24 ;  how  many  has  each  ? 

5.  Alice  has  7  pins  more  than  Abner,  and  both  have 
29  ;  how  many  has  each  ? 

6.  f  of  |  is  |  of  what  number  ? 

7.  The  sum  of  two  numbers  is  36,  and  their  differ- 
ence is  16  ;  what  are  the  two  numbers  ? 

8.  A  boy  bought  f-  of  a  melon  for  8J  cents;  how 
much  is  that  for  1  melon  ? 

9.  Homer  and  Hannah  each  bought  an  equal  num- 
ber of  peaches ;  on  their  way  home  Hannah  had  4 
more  given  to  her,  then  together  they  had  24  : 
how  many  did  each  buy  ? 

10.  Two  boys"  had  each  an  equal  number  of  blocks; 
one  lost  4 ;  and  together  they  then  had  only  1 2 
remaining  :  how  many  had  each  at  first  ? 

n.  A  wagon  was  sold  for  $17f,  which  was  f  as 
much  as  it  cost ;  what  did  it  cost  ? 

1 2.  Hiram  had  twice  as  many  strawberries  as  Eugene, 
and  both  had  18  pints ;  how  many  had  each  ? 

13.  Ida  had  6  cents  more  than  twice  as  many  as  Ira, 
and  both  had  36  ;  how  many  had  each  ? 

14.  Susan  had  \  as  many  cents  as  Sarah  ;   Sarah  lost 


ALGEBRAIC     QUESTIONS.  117 

10  ;  then  together  they  had  50  ;    how  many  had 
each  at  first  '$ 

15.  Thomas  was  returning  from  market  with  twice 
as  many  eggs  as  Timothy ;    Thomas  broke  4  of 
his,  and  Timothy  6  of  his  ;  they  then  had  50  eggs 
remaining.     How  many  had  each  at  first  ? 

1 6.  §  of  a  number +14=44;  what  is  that  number  ? 

17.  A  boy  being  asked  his  age,  replied,  3  times  my 
age  —  7  years  are  23  years ;  how  old  was  he  ? 

1 8.  Mr.  A.,  being  asked  how  much  money  he  had, 
replied,  twice  what  I  have  -f  $60,  is  four  times 
$400  ;  how  much  money  had  A.  ? 

19.  Two  boys  have  49  marbles,  but  the  first  has  7  the 
most ;  how  many  has  each  ? 

20.  A  man  bought  a  sheep,  a  cow,  and  a  horse  for 
$70  ;  the  cow  cost  $10  more  than  the  sheep,  and 
the  horse  cost  $20  more  than  the  cow.     What 
was  the  cost  of  each  ? 

21.  A  man  bought  a  melon  for  18 f  cents,  which  was 
only  |  as  much  as  his  dinner  cost ;  what  was  the 
cost  of  his  dinner  ? 

22.  A  gentleman  bought  a  watch  and  chain  for  $80  ; 
the  chain  cost  J  as  much  as  the  watch ;  what  was 
the  cost  of  each  ? 

23.  A  farmer  bought  a  plow,  a  harness,  and  a  horse 
for  $58 ;  for  the  harness  he  gave  $6  more  than 
for  the  plow,  and  for  the  horse  $34  more  than  for 
the  harness.     How  much  did  he  give  for  each  ? 

24.  A  boy  bought  twice  as  many  oranges  as  lemons, 
and  on  his  way  home  ate  4  oranges  and  gave  6 
away ;  and  was  surprised  to  find  he  had  only  14 
oranges  remaining.     How  many  of  each  kind  did 
he  buy  ? 

2*j.  5  times  a  certain  number  —  12  is  48  ;  what  is 

that  number  ? 
2§.  §  of  a  certain  number  —  5  is  40  ;  what  is  that 

number  ? 


118  ALGEBRAIC     QUESTIONS. 

27.  A  boy,  being  asked  his  age,  replied,  11  years  are 
7  years  more  than  |-  of  my  age  ;  how  old  was  he  ? 

28.  A  boy,  being  asked  how  many  sheep  his  father 
had,  replied,  40  are  5  less  than  f  of  his  father's 
number ;  how  many  had  he  ? 

29.  A  boy  bought  18  lemons ;  for  f  of  them  he  paid 
3  cents  for  2,  and  for  the  remainder  he  paid  3 
cents  each ;  for  what  must  he  sell  them  each  to 
gain  10  cents  on  the  whole  ? 

30.  James,    John,    and    Joseph    together    have    96 
peaches ;    James   has   2   more   than   John,   and 
Joseph  has  as  many  as  both  James  and  John : 
how  many  has  each  ? 

31.  Henry  bought  54  oranges ;  for  §  of  them  he  paid 
2  cents  for  3,  and  for  the  remainder,  3  cents  for 
2  ;  and  sold  -J-  of  them,  at  the  rate  of  2  cents  for 
3,  and  the   remainder,  at  3  cents  for  2.     How 
much  did  he  gain  by  so  doing  ? 


LESSON     LI. 

1.  If  a  man  can  do  a  certain  piece  of  work  in  12 
days,  what  part  of  it  can  he  do  in  1  day  ? 

2.  If  a  man  can  drink  a  barrel  of  beer  in  20  weeks, 
what  part  of  it  can  he  drink  in  1  week  ? 

3.  If  it  require  9  hours  to  empty  a  vessel,  what  part 
of  it  can  be  emptied  in  1  hour  ? 

4.  If  a  family  consume  a  barrel  of  pork  in  30  days, 
what  part  of  a  barrel  do  they  daily  consume  ? 

5.  If  it  require  19  days  to  perform  a  certain  journey, 
what  part  of  it  can  be  performed  in  1  day  ? 

6.  If  A.  can  do  a  certain  piece  of  work  in  8  days, 
and  B.  could  do  the  same  in  12  days ;  what  part 
of  it  can  each  do  in  a  day  ? 

7.  If  C.  could  mow  a  certain  field  in  4  days,  and  p. 
could  do  the   same   in   6  days,  what   part   of  ii 


ALGEBKAIC     QUESTIONS.  119 

could  each  do  in  a  day  ?     How  much  could  they 
together  do  in  a  day  ? 

8.  If  C.  and  D.  can,  in  1  day,  mow  -f%  of  a  field,  how 
long  would  it  take  them  to  mow  the  whole  field  ? 

9.  How  many  days  would  it  take  to  perform  a  cer- 
tain piece  of  work,  if  -f%  of  it  can  "be  performed  in 
1  day? 

ro.  If  George  can  do  a  certain  piece  of  work  in  3 
days,  and  Granvil  in  6  days ;  how  long  will  it 
take  them  together  to  do  the  work  ? 

11.  If  James  can  eat  a  bushel  of  apples  in  10  days, 
and  Hud  in  12  days;  how  long  would  1  bushel 
last  both  ? 

12.  A.  can  cut  a  field  of  wheat  in  12  days,  and  B. 
can  do  the  same  in  20  days ;  how  long  would  it 
take  them  to  cut  a  field  when  they  work  together  ? 

13.  A  merchant  bought  a  hogshead  of  molasses  for 
$20,  10  gallons  of  which  leaked  out ;  how  must 
he  sell  the  remainder  a  gallon  to  gain  $6.50  ? 

14.  |  of  a  barrel  of  flour  cost  $4|,  what  will  |  of  a 
barrel  cost  ? 

15.  A.  and  B.  can  build  a  boat  in  20  days,  and  with 
the  assistance  of  C.,  they  can  build  it  in  8  days. 
How  long  would  it  take  C.  to  build  it  aione  ? 

1 6.  A  farmer  and  his  son  can  do  a  piece  of  work  in 
6  days ;  the  son  can  do  the  same  in  27  days.    How 
long  would  it  take  the  father  to  do  the  work  2 

17.  Three  pipes,  A,  B,  and  C,  can  fill  a  cistern  in  2 
hours,  A  and  B  can  fill  it  in  4  hours,  and  A  and 
C  can  fill  it  in  3  hours.     How  long  would  it  take 
each  to  fill  it  ? 

1 8.  If  a  barrel  of  beer  would  last  a  man  35  days,  and 
the  man  and  his  son  20  days ;  how  long  would 
it  last  the  son  alone  ? 

19.  A  box  of  tea  usually  lasted  a  man  and  his  wife  9 
months;  when  the  man  was  absent  it  would  last 
the  wife  12  months.     How  long  would  it  have 
lasted  the  man  alone  ? 


120  ALGEBRAIC     QUESTIONS. 

20.  A.,  B.,  and  C.  can  build  a  boat  in  20  days,  A.  and 
B.,  in  40  days,  and  A.  and  C.,  in  30  days.     How 
long  would  it  take  each  separately  to  build  it  ? 

21.  Provided  A.  could  drink  a  barrel  of  beer  in  24 
days,  and  B.,  in  36  days ;  how  long  would  it  take 
them  together  to  drink  a  barrel,  after  f  of  it  had 
leaked  out  ? 

22.  A  market-woman  bought  30  oranges,  and  had  J 
of  them  stolen  ;  the  remainder  she  sold  at  3  cents 
each,  and  thereby  gained  f  of  a  cent  on  each 
orange  bought     How  much  did  they  cost  each  ? 

23.  A.  can  do  a  certain  piece  of  work  in  4-}  days,  and 
A.  and  B.  together  in  3  days.     Alter  A.  did  J 
of  the  work,  B.  did  the  remainder ;  how  long  did 
it  take  him  ? 

24.  If  A.  can  do  a  certain  piece  of  work  in  f  of  a  day, 
how  much  can  he  do  in  1  day  ? 

25.  If  a  man  can  chop  a  cord  of  wood  in  f  of  a  day, 
how  much  can  he  chop  in  1  day  ? 

26.  Isaac  can  make  a  pair  of  boots  in  |  of  a  day,  and 
Ira  in  |  of  a  day ;  how  many  pair  can  both  make 
in  a  day  ? 

27.  Samuel  can  cut  a  cord  of  wood  in  f  of  a  play,  and 
Theodore  in  f  of  a  day  ;   how  long  would  it  take 
them  to  cut  a  cord,  when  they  worked  together '] 

28.  If  §  of  an  ftpple  cost  f  of  a  cent,  what  will  f  of 
an  apple  cost '( 

29.  A.  can  mow  1  acre  of  grass  in  §  of  a  day,  B.,  in  f 
of  a  day,  and  C.,  in  f  of  a  day.    How  much  more 
can  A/and  B,  mow  in  a  day  than  C.  \ 

30.  If  a  wolf  can  eat  a  sheep  in  J  of  an  hour,  and  a 
bear  can  eat  it  in  j  of  an  hour,  how  long  would 
it  take  them  together  to  eat  what  remained  of  a 
sheep  after  the  wolf  had  been  eating  \  of  an  hour  ? 

NOTE. — The  wolf  in  £  hour  can  eat  4  of  the  sheep,  and 
in  1  hour  he  can  eat  f  of  a  sheep.  The  bear  in  1  hour 
can  eat  -f  of  a  sheep.  Therefore,  in  1  hour  both  can  eat 
|  + 1— |i  of  a  sheep.  Therefore,  to  eat  f — 4=^-  of  a  eheep, 
it  .vi  11  require  -^  of  an  hour  =10  min.  23^  sec. 


ALGEBRAIC    QUESTIONS.  121 


LESSON     LII. 

x.  Lewis,  meeting  some  beggars,  gave  each  of  them 
2  sents,  and  had  12  cents  remaining ;  if  he  had 
given  them  4  cents  each,  it  would  have  taken  all 
the  money  he  had.  How  many  beggars  were  there  ? 

ANALYSIS. — By  the  last  condition  of  the  question,  he  gave* 
each  beggar  2  cents  more  than  by  the  first,  and  to  them  all, 
12  cents  more  than  by  the  first  condition.  Therefore,  there 
must  have  been  as  many  beggars  as  2  is  contained  times  in 
12,  which  are  6  beggars." 

2.  A  boy  gave  to  each  of  his  playmates  3  cents,  and 
had  24  cents  remaining ;    if  he  had  given  them 
each  7  cents,  it  would  have  taken  all  the  money 
he  had.     How  many  playmates  had  he  ? 

3.  Mary  gave  each  of  her  playmates  5  apples  ;  if  she 
had  given  them  each  7  apples,  it  would  have  taken 
12  apples  more.     How  many  playmates  had  shel 

4.  A  number  of  persons  gave  me  10  cents  each;  had 
they  given   me   12    cents   each,   it  -would    have 
amounted  to  20   cents   more.      How  many  per- 
sons were  there  ? 

5.  I  of  $100  is  ^f  -5-  of  \  times  the  salary  of  the  Pres- 
ident of  the  United  States  ;  what  is  his  salary  ? 

6.  $10  is  |  times  ^  of  the  salary  of  the  Vice-Pres- 
ident of  the  United  States ;  what  is  his  salary  ? 

7.  Divide  35  oranges  between  James  and  Joseph,  so 
that  James  may  have  15  more  than  Joseph. 

8.  A  cask  of  wine  was  sold  for  $96,  which  was  f  of 
twice  as  much  as  it  cost;  how  much  did  it  cost  ? 

9.  By  selling^  quantity  of  cotton  for  $560,  I  gained 
|  of  what  it  cost ;  how  much  did  it  cost  ? 

10.  A.  and  B.  are  187  miles  apart,  and  are  traveling 
towards  each  other,  one  at  the  rate  of  8  miles  an 
hour,  and  the  other,  9  miles  an  hour ;  how  many 
hours  before  they  meet  ? 


122  ALGEBKAIC     QUESTIONS. 

1 1 .  Agnes  gave  2  dimes  a  yard  for  a  piece  of  calico ; 
had  she  given  3  dimes  a  yard,  it  would  have  cost 
20  dimes  more ;  how  many  yards  did  the  piece 
contain  ? 

12.  A.  was   ordered   to   buy   a   certain    number  of 
oranges ;   if  he  bought  those,  at  2  cents  each,  he 
would  have  had  no  money  left ;    if  he  bought 
those  at  3  cents  each,  he  would  have  wanted  10 
cents  more  to  have  paid  for  them.     How  many 
oranges  was  he  required  to  buy  ? 

13.  A  lady  wished  to  buy  a  certain  number  of  yards 
of  muslin .;  there  wrere  two  kinds,  some  at  9  cents 
a  yard,  and  some  at  12  cents  a  yard.     Had  she 
taken  that  at  12  cents  a  yard,  it  would  have  cost 
36  cents  more  than  the  other  kind.     How  many 
yards  did  she  wish  to  buy  ? 

14.  A  boy  being  sent  to  market  to  buy  a  certain 
number  of  pounds  of  meat,  found,  if  he  bought 
beef  at  5  cents  a  pound,  he  would  have  39  cents 
remaining,  but  if  he  bought  pork  at  8  cents  a 
pound,  he  would  have  only  6  cents  remaining. 
For  how  much  meat  was  he  sent  ? 

15.  If  8  times  a  certain  number  is  36  more  than  5 
times  the  same  number,  what  is  that  number  ? 

1 6.  A  boy  being  asked  his  age,  said,  4  times  my  age 
is  24  years  more  than  2  times  my  age ;   how  old 
was  he  ? 

17.  A  boy,  being  asked  how  many  sheets  of  paper  he 
had,  said,  4  times  the  number  is  18  less  than  7 
times  the  number ;   how  many  sheets  of  paper 
had  he  ? 

1 8.  A  person,  wishing  to  buy  some  butter,  found,  if 
he  bought  that  which  was  10  cents  a  pound,  he 
would  have  20  cents  remaining ;  but  if  he  bought 
that  which  was  12  cents  a  pound,  he  would  lack 
14  cents  of  having  money  enough  to  pay  for  it. 
How  many  pounds  did  he  wish  to  buy « 


ALGEBRAIC     QUESTIONS.  123 

19.  A  fanner,  wishing  to  buy  a  certain  number  of 
sheep,  found  if  he  gave  $2  a  head,  he  would  have 
$20  remaining;   but  if  he  gave  $5  a  head,  he 
would  lack  $40  of  having  money  enough  to  pay 
for  them.     How  many  sheep  did  he  wish  to  buy  ? 

20.  A.,  B.,  and  C.,  talking  of  their  ages;  says  A.  to 
B.,  I  am  4  times  as  old  as  you  ;   says  B.  to  C.,  I 
am  J  as  old  as  you  ;   but  says  A.  to  C.,  I  am  40 
years  older  than  you.     Required  the  age  of  each. 


LESSON     LIII. 

1.  A  laborer  agreed  to  work  40  days  upon  this  con- 
dition :  that  f$r  every  day  he  worked  he  should  re- 
ceive $2,  and  for  every  day  he  was  idle  he  should 
pay  $1  for  his  board.    At  the  expiration  of  the  time, 
he  received  $50.     How  many  days  did  he  work  \ 

ANALYSIS. —  If  he  had  labored  the  whole  time,  he  would 
have  received  40  times  $2,  or  $80.  But  he  received  only 
$50 :  he,  therefore,  lost  by  his  idleness  $80  —  $50,  or  $30. 
For  every  day  he  was  idle  he  lost  $2  (his  daily  wages) +  $1 
(the  cost  of  his  board),  which  are  $3.  If  in  1  day  he  lose 
$3,  he  will  lose  $1  in  \  of  a  day,  and  $30  in  30  times  \  of  a 
ctay,  or  10  days.  Therefore,  he  was  idle  10  days,  and  worked 
46  —  10  days,  or  30  days. 

2.  A  man  agreed  to  work  60  days  on  this  condition  : 
that  for  every  day  he  worked  he  should  receive  $1^-, 
and  for  every  day  he  was  idle  he  should  pay  $ \  for 
his  board.     At  the  expiration  of  the  time,  he  re- 
ceived $68.     How  many  days  did  he  work  ? 

3.  A  man  was  hired  for  80  days,  on  this  condition  : 
that  for  every  day  he  worked  he  should  receive  6 
dimes,  and  for  every  day  he  was  idle  he  should 
forfeit  4  dimes.     At  the  expiration  of  the  time,  he 
received  $40.     How  many  days  did  he  work  ? 

4.  How  many  times  f  of  12*  is  \  of  48  ? 


124  ALGEBKAIO     QUESTIONS. 

5.  A.  and  B.  bought  a  quantity  of  flour  for  $50  ;  A. 
paid  $1  as  often  as  B.  f  of  a  dollar ;  what  part  of 
the  flour  belongs  to  each  ? 

6.  A.,  B.,  and  0.  built  a  house,  which  cost  $500,  of 
which  B.  paid  $100  more  than  A.,  and  C.  paid  as 
much  as  A.  and  B.  both ;  how  much  did  each  pay  ? 

7.  A  merchant  sold  a  quantity  of  cloth  for  $84,  and 
thereby  lost  f-  of  what  it  cost ;  what  did  it  cost  '$ 

8.  7-J  is  2-J-  times  f  of  how  many  times  1 J  ? 

9.  A  farmer  having  in  his  employ  an  equal  number 
of  men  and  boys,  gave  to  each  boy  $4,  to  each 
man  $8,  and  to  them  all,  $84 ;   how  many  men 
were  there  ? 

10.  Two  men  hired  a  pasture  for  $35  ;  one  put  in  3 
cows,  and  the  other  4  cows ;   jjow  much  ought 
each  to  pay  ? 

11.  A  man  sold  an  equal  number  of  ducks  and  tur- 
keys for  20  dimes ;  the  ducks  at  2  dimes  each,  and 
the  turkeys  at  3  dimes  each.     How  many  did  he 
sell  in  all  I 

12.  A  farmer  sold  an  equal  number  of  ducks  and  tur- 
keys ;  the  ducks  at  4  dimes  each,  the  turkeys  at 
7  dimes  each  ;  and  for  the  turkeys  he  received  $3 
more  than  for  the  ducks.     How  many  of  each 
did  he  sell  ? 

13.  There  are  two  baskets,  containing  37  apples;  in 
one  of  which  there  are  17  more  than  in  the  other. 
How  many  apples  in  each  ? 

14.  Charles  and  Henry  together  have   49  marbles, 
and  Charles  has  7  more  than  twice  as  many  as 
Henry.     How  many  has  each  ? 

15.  Philip  has  20  apples  more  than  Philo;   and  to- 
gether they  have  92  ;  how  many  has  each  ? 

1 6.  Three  boys  have  47  lemons ;  the  first  has  3  more 
than  the  second,  and  the  second  7  more  than  the 
third.     How  many  has  each  ? 

17.  A  boy  was  hired  for  20  days,  on  this  condition : 


ALGEBKAIO     QUESTIONS.  125 

that  for  every  day  he  labored  he  should  receive 
3  dimes,  and  for  every  day  he  was  idle  he  should 
pay  2  dimes  for  his  board.  At  the  expiration  of 
the  time  he  received  only  $1.  How  many  days 
was  he  idle  ? 

1 8.  A  boy  bought  a  whistle,  a  whip,  and  a  drum  for 
70  cents.     For  the  whip  he  gave  twice  as  much 
as  for  the  drum,  and  for  the  drum,  twice  as  much 
as  for  the  whistle  ;  how  much  did  he  give  for  each  ? 

19.  The  sum  of  three  numbers  is  54.     The  first  is 
twice,  and  the  third  3  times  the  second;   what 
are  those  numbers  ? 

20.  Sarah's  age  is  f  of  Susan's,  and  the  sum  of  their 
ages  is  24 ;  what  is  the  age  of  each  ? 

21.  ^  of  an  army  were  killed,  f  of  the  remainder 
taken  prisoners,   and  400  escaped :    how  many 
were  there  in  the  army  ? 


LESSON     LIY. 

1.  A  fishing  rod,  the  length  of  which  was  14>  feet, 
was  broken  into  two  pieces.     The  shorter  piece 
was  f  of  the  length  of  the  longer.     What  was  the 
length  of  each  piece  ? 

ANALYSIS. — f  of  the  length  of  the  longer  piece,  which  is 
the  length  of  the  shorter, +  £,  (the  length  of  the  longer)  =^ 
of  the  length  of  the  longer,  which  is  the  length  of  both,  or 
14  feet.  If  I  of  the  longer  is  14  feet,  £  is  -f  of  14  feet,  which 
is  2  feet,  and  £  (which  is  the  length  of  the  longer)  are  4 
times  2  feet,  or  8  feet.  14  —  8  —  6  feet,  the  length  of  the 
shorter  piece. 

2.  A  pole,  the  length  of  which  is  20  feet,  is  in  the  air 
and  water ;  f  of  the  length  in  the  air  equals  the 
length  in  the  water.     What  is  the  length  in  the 
air  and  water  respectively  ? 

3.  If  in  2  days  a  man  traveled  160  miles,  and  |  of 
the  distance  he  traveled  the  first  day,  equals  the 


126  ALGEBRAIC    QUESTIONS. 

distance  he  traveled  the  &3cond  day ;  how  far  did 
he  travel  each  day  ? 

4.  B.  and  C.  together  have  40  marbles ;   how  many 
has  each,  provided  |-  of  B.'s  number  is  equal  to  C.'s? 

5.  From  New  York  City  to  Redhook  is  100  miles, 
and  I  of  the  distance  from  New  York  to  Rhine- 
beck,  equals  the  distance  from  Rhinebeck  to  Red- 
hook.     How  far  from  Rhinebeck  to  New  York, 
and  how  far  from  Rhinebeck  to  Redhook  ? 

6.  If  a  horse  and  a  colt  were  worth  $90,  and   the 
horse  was  worth  1J  times   as   much  as  the  colt, 
what  was  the  value  of  each  ? 

7.  A  boy  paid  70  cents  for  a  slate  and  a  book ;  how 
much  did  he  pay  for  each,  provided  the  book  cost 
1 J  times  as  much  as  the  slate  ? 

8.  If  a  traveler  pay  $1.20  for  his  breakfast  and  din- 
ner, how  much  did  he  pay  for  each,  provided  his 
dinner  cost  |  as  much  as  his  breakfast  ? 

9.  A  pole,  the  length  of  which  is  67  feet,  is  in  the 
air  and  water ;  f  of  the  length  in  the  air  -f  7  feet 
ecmals   the   length   in  the  water.      Required  the 
length  in  the  air  and  in  the  water. 

10.  Divide  the  number  108  into  two  such  parts,  that 
£  of  the  first  +  8  shall  equal  the  second. 

1 1 .  Divide  the  number  97  into  two  such  parts,  that 
|-  of  the  first  +  7  shall  equal  the  second. 

1 2.  There  is  a  fish  the  length  of  which  is  18  feet ;  its 
tail  is  4  feet,  and  f  of  the  length  of  the  body 
equals  the   length  of  the   head.      What   is  the 
length  of  the  head  and  body  respectively? 

13.  There  is  a  fish  the  weight  of  which  is  11  pounds, 
and  \  of  the  weight  "of  the   head  +  8  pounds 
equals  the  weight  of  the  body ;  what  is  the  weight 
of  each  ? 

14.  A  ship-mast  51  feet  in  length,  was  broken  off  in 
a  storm,  and  f  of  the  length  broken  off,  equaled 
|  of  the  length  remaining ;  how  much  was  broken 
off.  and  how  much  remained  ? 


ALGEBRAIC     QUESTIONS.  127 

15.  A  boy  being  asked  how  many  apples  and  oranges 
lie  had,  answered,  in  all  I  have  36,  and  f  of  the 
number  of  apples  equals   J  of  the  number  of 
oranges  ;  how  many  of  each  kind  had  he  \ 

1 6.  |  of  one  number  equals  |  of  another,  and  their 
sum  is  57 ;  what  are  the  two  numbers  ? 

17.  A  farmer  has  290  sheep  in  two  different  fields ; 
and  f  of  the  number  in  the  first  field,  equals  f 
of  the  number  in  the  second ;    how  many  are 
there  in  each  field  ? 

1 8.  A  market  woman  was  requested  to  buy  33  fowls, 
consisting  of  two  kinds ;  J  of  the  number  of  the 
first  kind,  was  to  equal  f  of  the  number  of  the 
second  ;  how  many  of  each  must  fthe  buy  ? 

19.  A  person,  being  asked  the  time  of  day,  said,  the 
time  past  noon  is  \  of  the  time  past  midnight ; 
what  was  the  hour  \ 

REMARK. —  Since  the  time  past  noon  is  \  of  the  time 
past,  midnight,  the  time  from  midnight  to  noon,  which  ia 
12  hours,  must  be  f  of  the  time  past  midnight. 

20.  A  person,  being  asked  the  hour  of  the  day,  said, 
the  time  past  noon  is  \  of  the  time  past  midnight ; 
what  was  the  hour  ? 

21.  A  person,  being  asked  the  hour  of  the  day,  said, 
the  time  past  noon  is  \  of  the  time  from  now  to 
midnight ;  what  is  the  hour  ? 

ANALYSIS. — From  "  now  "  to  midnight  is  f ,  and  ^  added 
(the  time  past  noon)  is  |.  Consequently,  from  noon  to 
midnight  (which  is  12  hours)  is  f  of  the  time  itlacked  of 
being  midnight ;  and  ^  of  the  time  is  £  of  12,  which  is  3 
hours,  the  time  past  noon. 

22.  What  is  the  time  of  day,  provided  f  of  the  time 
from  now  to  midnight  equals  the  time  past  noon  ? 

23.  A  man,  being  asked  the  hour  of  the  day,  said,  | 
of  the  time  past  noon  equals  §  of  the  time  from 
now  to  midnight ;  what  was  the  time  ? 

A  pole,  the  length  of  which  was  68  feet,  was  in 
the  air  and  water;    |  of  the  length  in  the  air 


128  ALGEBRAIC     QUESTIONS. 

equaled  f  of  the  length  in  the  water.    What  was 
the  length  in  the  air  and  in  the  water  respectively  ? 

25.  The  sum  of  two  numbers  is  176,  and  f  of  the  first 
+  4  equals  |  of  the  second  ;  required  the  numbers. 

26.  A  person,  being  asked  the  time  of  day,  said,  -|  of 
the  time  past  midnight   equals  -£$  of  the   time 
from  now  to  midnight  again  ;  what  o'clock  is  it  ? 

27.  Provided  the  time  past  10  o'clock,  A.  M.,  equals  f 
of  the  time  to  midnight ;  what  o'clock  is  it  ? 

28.  Says  A.  to  B.,  f  of  my  age  4-  4  years  equals  f  of 
yours,  and  the  sum  of  our  ages  is  74  years ;  what 
is  each  of  their  ages  ? 

29.  A  person,  being  asked  the  hour  of  the  day,  re- 
plied, f  of  the  time  past  noon  equals  f  of  the 
time  from  now  to  midnight  +  2f  hours  ;   what 
was  the  time  ? 

30.  A  pole,  the  length  of  which  is  78  feet,  is  in  the 
air  and  water;   f  of  the  length  in  the  air  +  12 
feet,  equals  1^  times  the  length  in  the  water. 
What  is  the  length  in  the  air  and  water  respec- 
tively ? 


LESSON     LY. 

There  is  a  fish  the  head  of  which  is  4  inches  long, 
and  whose  tail  is  as  long  as  its  head  +  J-  of  its 
body,  and  whose  body  is  as  long  as  its  head  and 
tail ;  what  is  the  length  of  the  fish  ? 

ANALYSIS. —  By  a  condition  of  the  question,  £  of  the 
length  of  the  body  +  4  inches,  is  the  length  of  the  tail ;  to 
which  add  4  inches  (the  length  of  the  head),  and  we  have 
\  of  the  length  of  the  body  +  8  inches  ='  f ,  or  the  length  of 
the  body.  Therefore,  f  —  £,  or  \  of  the  length  of  the  body, 
equals  8  inches ;  and  f ,  or  twice  the  length  of  the  body, 
which  is  the  length  of  the  fish,  equals  4  times  8  inches,  or 
82  inches. 

The  head  of  a,  fish  is  6  inches  long,  its  tail  is  as 
long  as  its  head  -f  \  of  its  body,  and  the  body  is 


ALGEBRAIC     QUESTIONS.  129 

as  long  as  the  head  and  tail  together ;  what  is  the 
length  of  the  fish  2 

3.  The  head  of  a  fish  is  12  inches  long,  the  tail  is  as 
long  as  the  head  +  £  of  the  body,  and  the  body 
is  as  long  as  the  head  and  tail ;  what  is  the  length 
of  the  fish  ? 

4.  The  head  of  a  fish  weighs  10  pounds,  the  tail 
weighs  as  much  as  the  head  +  f  as  much  as  the 
body,  and  the  body  weighs  as  much  as  the  head 
and  tail ;  what  is  the  weight  of  the  tail  ? 

5.  f  of  a  certain  number  equals  f  of  the  same  num- 
ber +  10 ;  what  is  that  number  ? 

6.  A  boy,  being  asked  his  age,  replied,  §  of  my  age 
exceeded  |  of  my  age  by  4  years ;  how  old  was  he  ? 

7.  James,  being  asked  how  many  arithmetical  ques- 
tions he  had  answered  correctly  during  the  week, 
replied,  f  of  the  number  is  3  more  than  |  of  the 
number ;  how  many  questions  had  he  answered  ? 

8.  A  farmer,  after   selling  f  of  1J  times  as  much 
grain  as  he  hud,  had  80  bushels  remaining ;  how 
much  had  he  at  first  ? 

9.  An  individual,  after  spending  f  of  all  his  money, 
and  f  of  what  then  remained,  had  only  $12|  re- 
maining ;  how  much  had  he  at  first  ? 

10.  If  f  of  a  ship  be  worth  -£  of  her  cargo,  which  is 
valued  at  300  Eagles,  what  is  the  value  of  the 
ship  ? 

11.  Dick  being  asked  how  much  money  he  had,  said, 
its  J  exceeded  its  f  by  $2 ;  how  much  had  he  ? 

1 2.  A  tree,  by  falling,  was  broken  into  three  pieces ; 
the  top  part  was  10  feet  long,  the  bottom  part 
was  as  long  as  the  top  -f  |  of  the  middle,  and  the 
middle  part  was  as  long  as  the  other  two ;  what 
was  the  length  of  the  tree,  and  of  each  piece  ? 

13.  A  man  bought  a  hat,  a  coat,  and  a  watch ;  the 
hat  cost  $6,  the  watch  cost  as  much  as  the  hat 
+  |  of  the  cost  of  the  coat,  and  the  coat  cost  as 


130  ALGEBRAIC     QUESTIONS. 

much  as  the  hat  and  watch ;  what  was  the  cost 
of  each,  and  of  all  ? 

14.  |  of  f  is  how  many  times  |  of  T5g  ? 

15.  If  |  of  a  ton  of  hay  cost  f  of  an  Eagle,  how  many 
dollars  will  ^  of  a  ton  cost  ? 

1 6.  A  third  and  J  of  a  third  of  10  is  f  of  what  number  ? 

1 7.  If  from  a  certain  number  you  take  its  J  and  its  J, 
the  remainder  will  be  13f ;  what  is  that  number? 

1 8.  After  spending  f  of  my  money,  I  earned  §  as 
much  as  I  spent,  and  then  had  only  $20  less  than 
what  I  had  at  first ;  how  much  had  I  at  first  ? 

19.  The  head  of  a  fish  is  8  inches  long,  the  tail  is  as 
long  as  the  head  and  J  of  the  body  -f- 10  inches, 
and  the  body  is  as  long  as  the  head  and  tail ; 
what  is  the  length  of  the  fish  ? 

20.  The  head  of  a  fish  is  12  inches  long ;  its  tail  is  10 
inches  longer  than  its  head  increased  by  ^  the 
length  of  the  body,  and  its  body  is  20  inches 
longer  than  its  head  and  tail  together ;  what  is 
the  length  of  the  fish  ? 


LESSON     LYI. 

1.  James  is  20  years  old,  and  John  is  4  years  old ;  in 
how  many  years  will  James,  wrho  is  now  5  times 
as  old  as  John,  be  only  twice  as  old  ? 

REMARK. — Four  years  ago  James  was  16,  and  in  16  years 
more  be  will  J)e  twice  as  old  as  John. 

2.  Sarah  is  10  years  old,  and   Sally  is  4 ;    in  how 
many  years  will  Sally  be  ^  as  old  as  Sarah  ? 

3.  Jacob  is  40  years  old,  and  Alfred  is  2  ;    in  how 
many  years  will  Alfred  be  J  as  old  as  Jacob  \ 

4.  If  a  third  of  6  be  3,  what  will  J  of  20  be  ? 

5.  If  3  be  a  third  of  6,  what  will  J  of  20  be  ? 
.6.  If  I  of  12  be  10,  what  will  f  of  10  be  ? 


ALGEBRAIC     QUESTIONS.  131 

7.  Divide  the  number  85  into  two  parts,  that  shall 
be  to  each  other  as  |  to  f . 

8.  When  A.  was  married,  he  was  3  times  the  age  of 
his  wife,  but  15  years  after  their  marriage  his  age 
was  only  twice  her  age ;  how  old  was  each  when 
they  were  married  ? 

REMARK. — The  conditions  of  the  above  question  give 
the  following : 

9.  Three  times  a  certain  number  -f  15  equals  twice 
the  same  number  +  30  ;   what  is  that  number, 
and  what  is  3  times  the  same  number  ? 

10.  Once  a  certain   number  +  15   equals   f    of  the 
same  number  +  30 ;    what  is  that  number,  and 
what  is  j  of  the  same  number  ? 

11.  When  I  first  met  Mr.  A.,  I  was  ^  as  old  as  he 
was,  and  in  12  years  after  that  I  was  f  as  old  as 
he  was ;   what  was  each  of  our  ages  when  we 
first  met  ? 

12.  There  are  two  numbers,  one  of  which  is  4  times 
the  other ;  but  if  to  each  20  were  added,  one  will 
be  double  the  other;  what  are  these  numbers? 

13.  When  B.  was  married  he  was  3  times  as  old  as 
his  wife ;   but  after  they  had  been  married  60 
years,  |  of  his  age  equaled  hers ;  what  was  the 
age  of  each  when  they  were  married  ? 

14.  A  hound  takes  3  leaps  to  a  fox  4,  and  3  of  the 
hound's  leaps  are  equal  to  6  of  the  fox's;  how  many 
leaps  must  the  hound  take  to  gain  1  on  the  fox  ? 

15.  If  the  hound  takes  1 J  leaps  to  gain  1  on  the  fox, 
how  many  must  he  take  to  gain  20  on  the  fox  ? 

1 6.  A  hare  is  20  leaps  before  a  hound,  and  takes  4 
leaps  to  the  hound  3  ;  and  3  of  the  hound's  leaps 
are  equal  to  6  of  the  hare's.     How  many  leaps 
must  the  hound  take  to  catch  the  hare  ? 

17.  A  fox  is  60  leaps  before  a  hound,  and  takes  5 
leaps  to  the  hound  2 ;  and  4  of  the  hound's  leaps 
equals  12  of  the  fox's.    How  many  leaps  must  the 
hound  take  to  catch  the  fox  ? 


132  ALGEBRAIC     QUESTIONS. 

1 8.  Alfred  is  60  steps  before  Silas,  and  takes  9  steps 
to  Silas  G  ;   and  3  of  Silas's  steps  equals  T  of 
Alfred's.    How  many  steps,  at  this  rate;  will  each 
take  before  they  will  be  together  ? 

REMARK. — A  lox  of  glass  contains  50  square  feet,  as  nearly 
as  may  be. 

19.  How  many  panes  of  glass  in  a  box,  provided  they 
are  6,  by  8  inches  ? 

REMARK. — Find  tlie  area  of  a  pane  of  glass  by  reducing 
the  inches  to  parts  of  a  foot,  and  then  multiply  these 
parts  together.  The  area  of  a  pane  6  by  8  inches  is  $  of 
a  square  foot.  The  remainder  may  be  solved  as  follows : 

ANALYSIS. — If  to  make  £  of  a  square  foot  it  require  1 
pane,  to  make  f ,  or  1  square  foot,  it  will  require  3  times 
1,  or  3  panes;  and  to  make  50  square  feet  (1  box),  it  will 
require  50  times  3  panes,  which  are  150  panes. 

20.  How  many  panes  of  glass  in  a  box,  provided  they 
are  8,  by  10  inches  ? 

21.  How  many  panes  of  glass  in  a  box,  provided  they 
are  10,  by  12  inches  ? 

22.  How  many  panes  of  glass  in  a  box,  provided  they 
are  8,  by  12  inches  ? 

23.  How  many  panes  of  glass  in  a  box,  provided  they 
are  12,  by  15  inches? 


LESSON     LYII. 

1.  What  number  is  that,  to  which  if  its  J  be  added, 
the  sum  will  be  15  ? 

2.  What  number  is  that,  to  which  if  its  J  be  added, 
the  sum  will  be  24  ? 

3.  What  number  is  that,  to  which  if  its  £  be  added, 
the  sum  will  be  40  ? 

4.  What  number  is  that,  to  which  if  its  ^  be  added, 
the  sum  will  be  30  ? 

5.  What  number  is  that,  to  which  if  its  f  be  added, 
the  sum  will  be  88  3 


ALGEBRAIC     QUESTIONS.  133 

6.  How  old  is  that  man,  to  whose  age  if  you  add 
its  J  and  its  f ,  the  sum  will  be  104  years  ? 

7.  What  number  is  that,  which  being  increased  by 
its  -J,  its  J,  and  18  more,  will  be  doubled  ? 

8.  A'  man,  being  asked  his  age.  said,  my  age  in- 
creased by  its  f  and  20  more,  is  double  my  age. 
What  was  his  age  ? 

9.  Suppose  I  buy  a  certain  number  of  boxes  of  but- 
ter, at  $2  a  box,  as  many  more  at  $4  a  box,  and 
sell  them  all  at  $3  a  box ;  do  I  gain  or  lose,  and 
how  much  ? 

10.  A  boy,  being  asked  how  many  oranges  he  had, 
replied,  if  my  number  were  increased  by  its  f ,  its 
|,  and  42  more,  the  sum  would  equal  3  times  my 
number.     How  many  had  he  ? 

11.  Suppose   I  buy  a   certain   number  of   melons; 
some  at  10  cents  each,  and  as  many  more  at  40 
cents  each ;  and  sell  them  all  at  30  cents  each ; 
how  much  do  I  gain  on  each  melon  ? 

1 2.  If  by  selling  1  apple  I  lose  -2%  of  a  cent,  how  many 
apples,  at  this  rate,  must  I  sell  to  lose  6  cents  ? 

13.  A  boy  bought  a  certain  number  of  lemons,  at  2 
cents  each,  as  many  more  at  4  cents  each ;  and 
sold  them  at  the  rate  of  3  for  5  cents :   did  he 
gain  or  lose,  and  how  much  ? 

14.  A  woman  bought  a  certain  number  of  apples,  at 
the  rate  of  2  for  a  cent,  as  many  more  at  the  rate 
of  3  for  a  cent ;  and  sold  them  all  at  the  rate  of  5 
for  2  cents,  and  by  so  doing,  lost  4  cents.     How 
many  of  each  kind  did  she  buy  ? 

15.  A  woman  bought  a  certain  number  of  eggs,  at 
the  rate  of  3  for  a  cent,  as  many  more  at  4  for  a 
cent ;   and  sold  them  out  at  the  rate  of  8  for  3 
cents,  and  by  so  doing,  gained  4  cents.-    How 
many  eggs  did  she  buy  '{ 

1 6.  Three  men  agreed  to  share  $510  in  the  propor- 
tion of  J,  |,  and  \ ;  how  much  must  each  receive  ? 


134  ALGEBKAIC    QUESTIONS. 

17.  A.'s  money  is  to  B.'s  as  \  is  to  J  ;  and  they  to- 
gether have  $100  ;  how  much  has  each  ? 

1 8.  The  difference  of  two  numbers  is  15,  which  is  | 
of  twice  as  much  as  the  smaller  number ;  what 
are  these  two  numbers  ? 

19.  A  merchant  bought  a  number  of  yards  of  cloth, 
at  the  rate  of  2  yards  for  $1,  and  as  many  more, 
at  the  rate  of  5  yards  for  $1 ;  and  sold  all  the 
cloth  at  the  rate  of  10  yards  for  $3  ;  and  thereby 
lost  $8.     How  many  yards  did  he  buy  ? 

20.  A  man  bought  a  certain  number  of  melons,  at 
the  rate  of  £  for  $1,  as  many  more  at  the  rate  of 
10  for  $1 ;  and  sold  them  all  at  the  rate  of  8  for 
$2,  and  thereby  gained  $6.     How  many  melons 
did  he  buy  ? 


LESSON     LVIII. 

1.  Mary  has  twice  as  many  apples  as  Sarah,  and  to- 
gether they  have  12  ;  how  many  has  each  ? 

REMAKE,  -By  the  condition  of  the  question,  Mary  has  2 
apples  as  often  as  Sarah  1.  Consequently,  Mary  must  have 
f ,  and  Sarah  ^  of  the  12  apples. 

2.  Divide  18  into  2  such  parts,  that  one  shall  be  twice 
the  other. 

3.  Divide  21  oranges  between  two  boys,  so  that  one 
may  have  twice  as  many  as  the  other. 

4.  Franklin  and  Francis  together  have  15  quarts  of 
nuts,  but  Franklin  has  twice  as  many  as  Francis ; 
how  many  quarts  has  each  ? 

5.  Robert  has  twice  as  many  cents  as  Harry,  and  to- 
gether they  have  24 ;  how  many  has  each  ? 

6.  Divide  the  number  27  into  two  parts,  that  shall 
be  to  each  other  as  1  to  2. 

7.  Harriet  is  twice  as  old  as  Ellen,  and  the  sum  of 
their  ages  is  30  years  ;  what  is  the  age  of  each  ? 


ALGEBRAIC    QUESTIONS.  135 

8.  A.  and  B.  are  36  rods  apart,  and  travel  towards 
each  other ;  how  far  will  each  travel  before  they 
meet,  provided  A.  travels  twice  as  fast  as  B.  ? 

9.  What  number  must  be  added  to  twice  itself,  that 
the  sum  may  be  57  ? 

10.  A.,  after  spending"  ^  of  all  his  money,  and  f  of 
the  remainder  less  $4,  had  only  $14  remaining ; 
how  much  had  he  at  first  ? 

11.  Divide  the  number  48  into  two  such  parts,  that 
one  shall  be  f  of  the  other. 

12.  In  a  certain  school,  there  are  3  times  as  many 
boys  as  girls,  and  in  all  there  are  52  pupils ;  how 
many  boys  and  how  many  girls  in  the  school  \ 

13.  James  and  Jackson  together  have  45  marbles, 
but  James  has  only  J  as  many  as  Jackson ;  how 
many  has  each '{ 

14.  A  man  and  his  son  together  earned  $280  in  a 
year ;  how  much  did  each  earn,  provided  the  boy 
earned  only  J  as  much  as  his  father  ? 

15.  A  boy  bought  a  melon  and  a  citron  for  $1 ;  how 
much  did  each  cost,  provided  the  melon  was  in 
value  only  J  as  much  as  the  citron  ? 

1 6.  A  man  bought  a  horse  and  a  saddle  for  $120 ; 
the  saddle  cost  only  -J  as  much  as  the  horse ;  what 
was  the  cost  of  each  't 

17.  A  man,  being  asked  the  cost  of  his  oxen,  said, 
my  oxen  and  wagon  together  cost  $240,  and  the 
oxen  cost  twice  as  much  as  the  wagon ;  what  was 
the  cost  of  each  ? 

1 8.  A  man  paid  for  a  sheep,  a  hog,  and  a  cow,  $42  ; 
for  the  hog,  he  gave  twice  as  much  as  for  the 
sheep,  and  for  the  cow,  3  times  as  much  as  for 
the  sheep.     How  much  did  he  give  for  each  ? 

19.  A   man    and  his   two   sons   earned   $560   in  1 
year;   the  father  earned  twice  as  much  as  his 
elder  son,  and  the  elder  son  earned  twice  as  much 
as  the  younger  son.     How  much  did  each  earn  ? 


136  ALGEBRAIC     QUESTIONS. 

20.  A.,  B.,  and  C.  together,  in  1  day,  can  dig  105 
bushels  of  potatoes ;  A.  can  dig  J  as  much  as  B., 
and  B.,  ^  as  much  as  C.     How  many  bushels  can 
each  dig  in  a  day  ? 

21.  A  man  bought  3  pieces  of  cloth  for  $160;  the 
first  piece  cost  only  J  as  much  as  the  second,  and 
the  second,  only  J  as  much  as  the  third.     How 
much  did  each  piece  cost  ? 

22.  In  an  array  consisting  of  20,000  men,  3  times  as 
many  were  wounded  as  were  killed,  and  4  times 
as   many   remained   unhurt   as   were   wounded. 
How  many  were  killed,  wounded,   and  unhurt 
respectively  ? 

23.  ^  of  A.'s  money,  +  f  of  B.'s  money  equals  $5500 ; 
and  §  of  B.'s  money  is  4  times  |  of  A.'s.     How 
much  money  has  each'? 

24.  Herman  and  Byron  together  have  60  blocks,  and 
Byron  owns  f  as  many  as  Herman ;  how  many 
has  each  ? 

25.  Divide  the  number  60  into  two  parts,  that  shall 
be  to  each  other  as  J  is  to  f  ? 

26.  Adelia  and  Louisa  are  to  share  14  apples  in  the 
proportion  of  4  to  3  ;   how  many  ought  each  to 
receive  ? 

27.  The  sum  of  Mary  and  Hezekiah's  ages  is  25  years ; 
how  old  is  each,  provided  Hezekiah  is  only  f  as 
old  as  Mary  ? 

28.  Henry  and  his  father  can  thrash  out  35  bushels 
of  oats  in  a  day ;  how  much  does  each,  if  Henry 
thrashes  out  only  f  as  much  as  his  father  ? 

29.  A  pole,  whose  length  is  TO  feet,  is  in  the  air  and 
water ;  how  much  is  in  the  air  and  water  respec- 
tively, if  f  of  the  length  in  the  air  equals  the 
length  in  the  water  ? 

30.  Divide  the  number  36  into  two  parts,  that  shall 
be  to  each  other  as  5  is  to  4. 

31.  Divide  the  number  45  into  two  parts,  that  shall 
be  to  each  other  as  1  is  to    . 


ALGEBRAIC     QUESTIONS.  137 

32.  A.  and  B.  together  own  $480 ;  but  A.  owns  only 
f  as  much  as  B. ;  how  much  belongs  to  each  ? 

33.  A  man  died,  and  left  $7200  to  be  divided  be- 
tween his  son  and  daughter,  in  the  proportion  of 
1  to  f .     How  much  ought  each  to  receive  ? 

34.  In  a  mixture  of  tea  consisting  of  48  pounds,  there 
was  J  as  much  poor,  as  good  tea  ;   how  much  of 
each  kind  was  there  ? 

35.  A  man  bought  a  cow  and  a  horse  for  $96 ;  the 
cow  cost  f  as  much  as  the- horse;  how  much  was 
the  cost  of  each  ? 

36.  Moses  has  only  f  as  many  chestnuts  as  Aaron,  and 
both  have  40  quarts  ;  how  many  quarts  has  each  ? 

37.  Divide  the  number  49  into  two  parts,  that  shall 
be  to  each  other  as  1  is  to  f . 

38.  A  hound  ran  60  rods  before  he  caught  a  fox,  and 
|  the  distance  the  fox  ran  before  he  was  caught, 
equaled  the  distance  he  was  ahead  when  they 
started.     How  far  did  the  fox  run,  and  how  far 
in  advance  of  the  hound  was  he,  when  the  chase 
commenced  ? 

39.  The  sum  of  two  numbers  is  140,  and  the  larger 
is  to  the  smaller  as  1  is  to  f ;  what  are  the  two 
numbers  ? 

40.  A.  and  B.  together  owe  $69,  but  B.  owes  only  ^ 
as  much  as  A. ;  how  much  does  each  owe  ? 

41.  Thomas  and  Thornton  found  $240,  but  could  not 
agree  about  the  division  of  it ;   they,  therefore, 
threw  it  on  the  floor,  and  each  got  what  he  could  ; 
it  so  happened  that  Thomas  got  only  -f  as  much 
as  Thornton.     How  much  did  each  get  ? 

42.  In  a  certain  school  consisting  of  48  pupils,  there 
"are  If  times  as  many  boys  as  girls  ;   how  many 
boys,  and  how  many  girls  are  in  the  school  ? 

43-  A  gold  and  a  silver  watch  were  bought  for  $160 ; 
the  silver  watch  cost  only  ^  as  much  as  the  gold 
one ;  how  much  was  the  cost  t)f  each  2 


138  ALGEBRAIC     QUESTIONS. 

44.  Divide  the  number  17  into  two  parts,  that  shall 
be  to  each  other  as  |  is  to  |. 

45.  A  farmer  had  180  sheep  in  two  fields,  and  \  of 
the  number  in  the  first  field  equaled  -J  of  the 
number  in  the  second ;  how  many  in  each  field  2 

46.  Divide  88  into  two  parts  that  shall  be  to  each 
other  as  §  is  to  £. 

47.  I  of  the  distance  a  hare  ran,  after  a  hound  started 
in  pursuit,  equaled  the  distance  she  was  before 
the  hound  when  they  started ;   how  far  did  the 
hare  run  before  she  was  caught,  provided  the 
hound  ran  80  rods  to  catch  the  hare  ? 

48.  A.  and  B.  started  from  the  same  point,  and  ran  in 
the  same  direction  ;  B.  ran  60  rods ;  then  T\  of 
the  distance  A.  had  run  equaled  the  distance  A. 
was  ahead  of  B.     How  much  did  A.  gain  on  B. 
in  running  60  rods  ? 

49.  A  fishing-rod,  the  length  of  which  is  24  feet,  is 
in  two  parts ;   -|  of  the  longer  part  equals  the 
length  of  the  shorter.     How  long  is  each  part  ? 

50.  A  hound  ran  90  rods  before  he  caught  a  deer ; 
the  deer  ran  44  times  as  far  as  it  was  ahead  of 
the  hound   when    they   started,   before   it   was 
caught.     How  far  ahead  of  the  hound  was  the 
deer  when  the  chase  commenced  ? 

51.  f  of  A.'s  number  of  sheep  +  f  of  B.'s  number, 
equals  900  ;  how  many  sheep  has  each,  provided 
|  of  B.'s  number  is  twice  §  of  A.'s  number  ? 


LESSON     LIX. 

A  person  had  two  silver  cups,  and  only  one  cover 
for  both.  The  first  cup  weighed  6  oz.  If  the  first 
cup  be  covered,  it  will  weigh  twice  as  much  as  the 
second,  but  if  the  second  cup  be  covered,  it  will 


ALGEBRAIC     QUESTIONS.  139 

weigh  3  times  as  much  as  the  first.     What  is  the 
weight  of  the  second  cup  and  cover  ? 

ANALYSIS. — By  the  last  condition  of  the  question,  3  times 
6  oz.,  the  weight  of  the  first  cup,  or  18  ounces,  equals  the 
weight  of  the  second  cup  and  cover.  Consequently,  the 
two  cups  and  cover  weigh  18  +  6  ounces,  which  are  24ounces.y 
And  by  the  first  condition,  the  first  cup  and  cover  weigh 
twice  as  much  as  the  second  cup.  Therefore,  the  24  ounces 
must  be  divided  into  two  parts,  which  are  to  each  other  as 
2  to  1.  One  of  these  parts  will  be  the  weight  of  the  second 
cup,  and  2  the  weight  of  the  first  cup  and  cover,  &c. 

2.  A  lady  has  two  silver  cups,  and  only  one  cover. 
The  first  cup  weighs  8  ounces.     The  first  cup  and 
cover  weigh  3  times  as  much  as  the  second  cup ; 
and  the  second  cup  and  cover  4  times  as  much  as 
the  first  cup.     What  is  the  weight  of  the  second 
cup  and  cover? 

3.  A  man  bought  a  hat,  a  coat,  and  a  vest  for  $40. 
The  hat  cost  $6 ;  the  hat  and  coat  cost  9  times  as 
much  as  the  vest.     What  was  the  cost  of  each  ? 

4.  A  boy  bought  a  squirrel,  a   rabbit,   and  a  bird. 
The  squirrel  cost  15  cts.     The  squirrel  and  rabbit 
cost  twice  as  much  as  the  bird ;  and  the  rabbit  and 
bird  cost  3  times  as  much  as  the  squirrel.     What 
was  the  cost  of  the  bird  and  rabbit  respectively  ? 

5.  A  farmer  bought  a  cow,  an  ox,  and  a  horse ;  the 
cow  cost  $20.     The  cow  and  ox  together  cost  3 
times  as  much  as  the  horse ;  the  ox  and  horse  to- 
gether cost  4  times  as  much  as  the  cow.   What  was 
the  cost  of  the  ox  and  horse  respectively  ? 

6.  A  man  bought  two  horses  and  a  saddle.     The 
younger  horse  cost  $40.    The  saddle  cost  f  as  much 
as  both  horses ;   and  the  younger  horse  cost  J  as 
much  as  the  other  horse  and  saddle  together.  What 
did  the  saddle  and  older  horse  cost  respectively  ? 

7.  A  man  traveled  three  successive  days.     The  first 
day  he  traveled  30  miles,  which  was  J  of  the  dis- 
tance he  traveled  the  other  two  days ;  and  4  times 


140  ALGEBRAIC     QUESTIONS. 

the  distance  he  traveled  the  second  day  equaled 
the  distance  he  traveled  the  first  and  third  days. 
How  far  did  he  travel  each  day  ? 

8.  A.  is  worth  $1000,  and  B.  and  C.  together  are 
worth  9  times  as  much  as  A. ;  and  C.  is  worth  J 
as  much  as  A.  and  B.     How  much  is  B.  and  C. 
worth  respectively  ? 

9.  A  coat  cost  $20,  and  a  vest  and  hat  together  cost 
5  times  as  much  as  the  coat ;  3  times  the  cost  of 
the  vest  equaled  the  cost  of  both  coat  and  hat. 
What  was  the  cost  of  the  vest  and  the  hat  ? 

10.  B.'s  harness  cost  $120,  which  was  |  of  the  cost 
of  his  horse  and  sleigh ;  and  the  harness  and  horse 
together  cost  twice  as  much  as  the  sleigh.     How 
much  did  the  horse  and  sleigh  cost  respectively  ? 

11.  A  pole  in  falling  broke  into  three  unequal  pieces. 
The  top  piece  was  8  feet  long,  which  was  £  of 
the  length  of  the  other  two  pieces ;  and  3  times 
the  length  of  the  bottom  piece,  equals  the  length 
of  the  other  two  pieces.    How  long  was  the  pole, 
and  how  long  was  each  piece  ? 

12.  Find  the  ages  of  A.,  B.,  and  C.,  by  knowing  that 
A.  is  20  years  old,  and  that  the  sum  of  B.  and 
C.'s  ages  is  4  times  A.'s  age ;  and  that  C.'s  age  is 
-i  of  the  sum  of  A.  and  B.'s  ages. 

13.  Find  the  fortunes  of  A.,  B.,  C.,  D.,  E.,  and  F.,  by 
knowing  that  A.  is  worth  $20,  which  is  \  as  much 
as  B.  and  C.  are  worth,  and  that  C.  is  worth  \  as 
much  as  A.  and  B. ;  and,  also,  that  if  19  times 
the  sum  of  A.,  B.,  and  C.'s  fortunes  were  divided 
in  the  proportion  of  |,  £,  and  J,  it  would  respec- 
tively give  |  of  D.'s,  |-  of  E.'s,  and  J  of  F.'s  fortune. 

14.  A.  and  B.  dug  100  rods  of  ditch  for  $100.     A. 
received  10  shillings  a  rod,  and  B.  6  shillings  a  rod. 
How  many  rods  did  each  dig,  provided  each  re- 
ceived $50.     Ans.  A.  dug  37J  rods,  and  B.  62J. 

NOTE. — $l=7s.  6d  in  Pa.  and  N.  J. ;  6s.  in  New  Eng.  States, 
Va.,  Ky.,  and  Tenn. ;  and  Ss.  in  N.  Y.,  Ohio,  and  N.  C.  currency. 


REDUCTION.  141 


LESSON     LX. 

REMARK. —  In  general  business  calculations  of  Interest, 
and  in  this  book,  30  days  to  a  month,  and  12  of  such 
months  to  a  year,  are  reckoned,  although  such  estimate 
would  not  be  proper  for  a  correct  result  in  a  question 
wherein  should  be  stated  any  of  the  months  which  contain 
31  days. 

1 .  Reduce  2  years  and  4  months  to  the  fraction  of  a 
year. 

ANALYSIS. — 4  months  is  what  part  of  a  year  ?  There  are 
12  months  in  1  year ;  therefore,  1  month  is  ^  of  a  year,  and 
4  months  are  4  times  Ty,  which  are  ^,  or  £  of  a  year.  In 
2£  years,  how  many  thirds  ?  In  one  there  are  f ;  therefore, 
3  times  the  number  of  whole  years  equal  the  number  of 
thirds.  3  times  2  are  6,  and  %  added  are  f  of  a  year. 

jjgir"  REMARK. — Always  reduce  a  fraction  to  its  lowest 
terms  before  performing  any  other  operation  with  it. 

If  the  pupil  can  not  readily  discover  the  greatest  num- 
ber that  will  divide  both  numerator  and  denominator,  with- 
out a  remainder,  he  should  continue  to  divide  by  any,  or 
the  least  number  that  is  contained  in  both  numerator  and 
denominator  without  a  remainder,  until  the  fraction  is  re- 
duced to  its  lowest  terms. 

2.  Reduce  1  year  and  3  months  to  the  fraction  of  a 
year. 

3.  Reduce  3  years  and  5  months  to  the  fraction  of  a 
year. 

4.  Reduce  4  years  and  10  months  to  the  fraction  of  a 
year. 

5.  Reduce  7  years  and  9  months  to  the  fraction  of  a 
year. 

6.  Reduce  8  years  and  8  months  to  the  fraction  of  a 
year. 

7.  Reduce  12  years  and  7  months  to  the  fraction  of  a 
year. 

8.  Reduce  11  years  and  11  months  to  the  fraction  of  a 
year. 


142  REDUCTION. 

9.  Reduce  6  years  and  6  months  to  the  fraction  of  a 
year. 

10.  Reduce  9  years  and  8  months  to  the  fraction  of  a 
year. 

11.  Reduce  2  years  4  months  and  15  days  to  the  frac- 
tion of  a  year. 

ANALYSIS. — 15  days  is  what  part  of  a  month  ?  There 
are  30  days  in  one  month ;  therefore,  1  day  is  -fa  of  a 
month,  and  15  days  are  15  times  ^,  which  are  £f ,  or  £  of 
a  month.  4$-  months,  or  f  months,  is  what  part  of  a  year  ? 
There  are  12  months  in  1  year;  therefore,  1  month  is -^ 
of  a  year,  and  %  of  a  month  is  £  of  -j^,  which  is  ^  of  a 
year;  and  9  halves  are  9  times  ^1¥,  which  are  /¥,  or  f  of  a 
year.  2f  years,  equal  -1/  years. 

12.  Reduce  4  years  7  months   and  6  days  to  the 
fraction  of  a  year. 

13.  Reduce  5  years  9  months  and  18  days   to  the 
fraction  of  a  year. 

14.  Reduce  1  year  7  months  and  18  days   to  the 
fraction  of  a  year. 

15.  Reduce   2  years  7  months   and  6  days   to  the 
fraction  of  a  year. 

REMARK. — Omitting  the  intermediate  steps  in  the  anal- 
ysis, we  have : 

ANALYSIS. —  6  days  is  ^  or  %  of  a  month.  7£  months 
equal  ^-  months.  -3^-  months  equal  f  of  a  year.  2f  years 
equal  *-/-  years. 

1 6.  Reduce  3  years  3  months  and  6  days  to  the  frac- 
tion of  a  year. 

17.  Reduce  5  years  4  months  and   24  days  to  the 
fraction  of  a  year. 

1 8.  Reduce  6  years  5  months  and  18  days  to  the 
fraction  of  a  year. 

19.  Reduce  7  years  11  months  and  6  days  to  the 
fraction  of  a  year. 

20.  Reduce  10  years  10  months  and  12  days  to  the 
fraction  of  a  year, 


PERCENTAGE  AND  INTEREST.     143 


LESSON     L  X  I. 

Interest  is  the  money  paid  for  the  use  of  money,  or  its 
equivalent. 

JPer  Cent.,  or  Rate  per  Cent,,  signifies  by  the  hun- 
dred. Thus,  by  6  per  cent,  is  meant,  6  pounds  on  100  pounds; 
$6  on  $100,  or  Tf^  =  -^  of  the  quantity. 

Per  cent,  is  now  generally  written  by  business  men  thus,  %. 
7$  meaning,  7  per  cent. 

The  Principal  is  the  sum  on  which  interest  is  paid. 

The  Amount  is  the  sum  of  the  principal  and  interest. 

1.  At  4  per  cent.,  what  part  of  the  principal  equals 
the  interest  ? 

ANALYSIS. — At  4  per  cent.,  -^£5-,  or  -fa  of  the  principal, 
equals  the  interest. 

2.  At  2  per  cent.,  what  part  of  the  principal  equals 
the  interest  ? 

3.  At  5  per  cent.,  what  part  of  the  principal  equals 
the  interest  ? 

4.  At  6  per  cent.,  what  part  of  the  principal  equals 
the  interest  ? 

5.  At  8  per  cent.,  what  part  of  the  principal  equals 
the  interest  ? 

6.  At  10  per  cent.,  what  part  of  the  cost  equals  the 
gain  ? 

7.  At  7  per  cent.,  what  part  of  the  principal  equals 
the  interest  ? 

8.  At  12  per  cent.,  what  part  of  the  cost  equals  the 
gain  ? 

9.  At  18  per  cent.,  what  part  of  the  principal  equals 
the  interest  ? 

10.  What  is  the  interest  of  $80  for  1  year,  at  15  per 
cent.  ? 

ANALYSIS.— At  15  T)er  cent.,  ^,  or  ^  of  the  principal, 
equals  the  interest.     ^  of  $80  is  §12,  the  interest. 

11.  What  is  the  interest  of  $120  for  1  year,  at  25  per 
cent.  2 


L44  PER     CENT. 

12.  What  is  the  interest  of  $510  for  1  year,  at  20  per 
cent.  ? 

13.  What  is  the  interest  of  $750  for  1  year,  at  24  per 
cent.  ? 

14.  A  man  paid  $120  for  a  wagon,  and  sold  it  at  a 
gain  of  30  per  cent. ;  how  much  was  his  gain  ? 

ANALYSIS. — If  he  gained  30  per  cent.,  he  gained  -j8^,  or 
-$>  of  the  cost,     -&  of  $120  is  $86,  the  gain. 

15.  A  tailor  sold  a  coat  that  cost  him  $25,  at  a  gain 
of,  32  per  cent. ;  how  much  did  he  gain  ? 

1 6.  A  man  sold  a  quantity  of  goods  mat  cost  him 
$S40,  at  a  gain  of  75  per  cent. ;  how  much  did 
lie  gain  ! 

17.  Edward  spent  85  per  cent,  of  $120  for  a  suit  of 
clothes.     How  much  did  his  clothes  cost  ? 

1 8.  Henry's  watch  cost  $180,  he  sold  it  at  a  loss  of 
15  per  cent. ;  how  much  did  he  receive  for  it  ? 

19.  A  boy  sold  a  quantity  of  candy  that  cost  50  cts., 
at  a  gain  of  1 20  per  cent. :  how  much  did  he  re- 
ceive for  them  ? 

20.  Jacob  sold  a  horse  that  cost  him  $240,  at  a  loss 
of  25  per  cent. ;  how  much  did  he  receive  for  the 
horse  ? 

LESSON     LXII. 

REMARK. — The  principal  or  cost  is  always  100  per  cent. 

1.  If  S3Q  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 

ANALYSIS  IST. — Ii'f\  of  the  principal  equals  the  interest, 
the  rate  per  cent,  is  -^  of  100  per  cent.,  which  is  6  per  cent. 

ANALYSIS  2c.— If  the  interest  of  1  cent  is  /7  of  a  cent,  the 
interest  of  100  cents  is  100  times  -^,  or  -3//,  or  6  cents. 

2.  Tf  -%\  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 

3.  If  ^  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 


PEE     CENT.  145 

4.  If  -5^  of  the  cost  equals  the  gain,  what  is  the  rate 

Eer  cent.  ? 
f  ^  of  the  cost  equals  the  gain,  what  is  the  rate 
per  cent.  ? 

6.  If  2*5  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 

7.  If  T\  of  the  cost  equals  the  gain,  what  is  the  rate 
per  cent.  ? 

8.  If  the  interest  of  $44  for  1  year  is  $4,  what  is  the 
rate  per  cent.  ? 

ANALYSIS. — If  the  interest  of  $44  is  $4,  ^,  or  ^  of  the 
principal  equals  the  interest.  Therefore,  the  rate  per  cent. 
is  -jij-  of  100  per  cent.,  which  is  9T'T  per  cent. 

9.  If  the  interest  of  $72  for  1  year  is  $6,  what  is  the 
rate  per  cent.  ? 

10.  If  the  interest  of  $96  for  1  year  is  $12,  what  is 
the  rate  per  cent.  1 

1 1.  B.  bought  a  horse  ror  $100,  and  sold  it  for  $109 ; 
how  much  did  he  gain  per  cent.  ? 

12.  A  woman  bought  a  quantity  of  oranges  for  75 
cents,  and  sold  them  for  84:  cents ;  how  much  did 
she  gain  per  cent.  ? 

13.  A  merchant  bought  a  quantity  of  books  for  $200, 
and  sold  them  for  $228 ;   how  much  did  he  gain 
per  cent.  ? 

14.  If  by  laying  out  $37,  I  gain  a  sum  equal  to  f  of 
it,  what  do  I  gain  per  cent.  ? 

15.  Harvey  bought  a  hogshead  of  malasses  for  $25, 
and  sold  it  for  $31| ;  how  much  did  he  gain  per 
cent.  ? 

1 6.  Bought  a  knife  for  37  cents,  and  sold  it  for  57J 
cents ;  what  was  the  gain  per  cent.  ? 

1 7.  A  stationer  sold  a  quantity  of  paper  for  |  of  what 
it  cost ;  how  much  did  he  gain  per  cent.  ? 

1 8.  James  received  for  his  horse  J  of  what  it  cost; 
how  much  did  he  gain  per  cent.  I 

7 


146  PEE,     CENT. 

19.  A  man  sold  a  barrel  of  pork  for  -J^-  of  what  it 
cost ;  how  much  did  he  gain  per  cent.  ? 

20.  The  interest  of  $500  for  4  years  is  $240 ;  what  is 
the  rate  per  cent.  ? 

ANALYSIS.— If  the  interest  of  $500  for  4  years  is  $240, 
for  1  year  it  is  £  of  $240,  or  $60.  Therefore,  /^,  or  in,  of 
the  principal,  equals  the  interest.  Hence,  the  rate  per 
cent,  is  y»y  of  100$,  which  is 


21.  A  man  being  asked  at  what  per  cent,  his  money 
was  on  interest,  replied,  I  receive  $120  interest 
in  10  years  for  $240  ;  what  was  his  rate  per  cent.  ? 

22.  A.  bought  a  horse  for  $150,  and  sold  it  for  $180? 
what  was  his  gain  per  cent.  ? 

23.  Elisha  bought  10  horses  for  $800,  and  sold  8  of 
them  for  what  all  cost ;  what  was  his  gain  per 
cent.  ? 

24.  -^y  of  the  money  which  C.  paid  for  books,  is  \  of 
what  he  gained  by  selling  them.     How  much  did 
he  gain  per  cent.  ? 

25.  28^  of  the  money  that  I  have  on  interest,  is  4  times 
the  yearly  interest  received.     What  is  the  rate 
per  cent.  ? 

26.  J|  of  the  cost  of  A.'s  merchandise,  is  f  of  what 
he  gained  when  he  sold  it.     What  was  his  gain 
per  cent.  ? 

27.  Y\  of  the  cost  of  B.'s  wagon  was  f  of  what  he 
gained  by  selling  it ;  what  did  he  gain  per  cent.  ? 

28.  A  book  was  sold  for  f  of  f  of  what  it  cost ;  what 
was  the  loss  per  cent.  ? 

29.  |  of  |  of  the  cost  of  a  sleigh,  was  what  the  sleigh 
sold  for ;  what  was  the  gain  per  cent.  ? 

30.  A  merchant  bought  a  quantity  of  goods  for  $860, 
and  sold  them  for  $1075 ;  how  much  did  he  gain 
per  cent.  I 


FEE  CENT  AGE.  147 

LESSON     LXIII. 

NOTE. — The  expression  of  a  certain  rate  per  cent.  (fc)  of  interest 
means  per  annum,  i.  e.,  for  a  year,  unless  otherwise  specified. 

1 .  At  5  per  cent,  for  4  years,  what  part  of  the  prin- 
cipal equals  the  interest  ? 

ANALYSIS. — If  the  interest  of  $1  for  1  year  is  5  cents,  for 
4  years  it  is  4  times  5  cents,  or  20  cents.  Therefore,  -f£Vt 
or  £  of  the  principal,  equals  the  interest. 

2.  At  6  per  cent,  for  5  years,  what  part  of  the  prin- 
cipal equals  the  interest  ? 

3.  At  3%  for  2  years,  what  part  of  the  principal 
equals  the  interest  ? 

4.  At  4^  for  3  years,  what  part  of  the   principal 
equals  the  interest  ? 

5.  At  6%  for  3  years,  what  part  of  the  principal 
equals  the  interest  ? 

6.  At  4%  for  3  years,  what  part  of  the  principal 
equals  the  interest  ? 

7.  At  9%  for  6  years,  what  part  of  the  principal 
equals  the  interest  ? 

8.  At  8$  for  5  years,  what  part  of  the  principal 
equals  the  interest  ? 

9.  At  4$  for  6  years,  what  part  of  the  principal 
equals  the  interest  ? 

10.  At  6%  for  8  years,  what  part  of  the  principal 
equals  the  interest  ? 

11.  At  10$  for  5  years,  what  part  of  the  principal 
equals  the  interest  ? 

12.  At  6%  for  4  years  and  8  months,  what  part  of 
the  principal  equals  the  interest  ? 

REMARK. — It  is  expected  that  pupils  understand  the  lessons 
before  this,  and  are,  therefore,  prepared  to  arrive  at  results, 
without  giving  the  analysis  of  all  parts  of  the  question. 

ANALYSIS.— 8  months  are  -fe,  ol>  I  of  a  Jea1'-  4f  years  equal 
•*/  years.  If  the  interest  of  $1  for  1  year  is  6  cents,  for  ^ 
years  it  is  ^-  times  6  cents,  or  28  cents.  Therefore,  -^  or  ^ 
of  the  principal,  equals  the  interest. 


148  INTEREST. 

13.  At  4:  per  cent,  for  6 -years  and  6  months,  what 
part  of  the  principal  equals  the  interest  ? 

14.  At  6  per  cent,  for  5  years  and  4  months,  what 
part  of  the  principal  equals  the  interest  ? 

15.  At  10^  per  cent,  for  1  year  and  6  months,  what 
part  of  the  principal  equals  the  interest  ? 

1 6.  At  4f  per  cent,  for  9  years,  what  part  of  the 
principal  equals  the  interest  I 

17.  At  3f  per  cent,  for  2  years  and  2  months,  what 
part  of  the  principal  equals  the  interest  ? 

1 8.  At  6J  per  cent,  for  4  months  and  24  days,  what 
part  of  the  principal  equals  the  interest  \ 

19.  At  7-J  per  cent,  lor  10  months,  what  part  of  the 
principal  equals  the  interest  ? 

20.  At  3-3*5$  for  2  years  4  months  and  15  days,  what 
part  of  the  principal  equals  the  interest  ? 


LESSON"     LXIY. 

r.  What  is  the  interest  of  $50  for  4  years,  at 

ANALYSIS  IST.  —  The  interest  of  $1  for  4  years,  at  6$,  is 
24  cents;  and  for  $50  it  is  50  times  24  cents,  or  $12. 

ANALYSIS  2D.  —  The  interest  of  $1  for  4  years,  at  6#,  is  24 
cents.  Therefore,  -?-£$,  or  /j  of  the  principal,  equals  the  in- 
terest. -fa  of  $50  is  $12,  the  interest. 


2.  What  is  the  interest  of  $10  for  2  years,  at 

3.  What  is  the  interest  of  $48  for  6  years,  at 

4.  What  is  the  interest  of  $70  for  7  years,  at  5$  ? 

5.  What  is  the  interest  of  $68  for  5  years,  at  6$  ? 

6.  What  is  the  interest  of  $70  for  2  years,  at  5$  ? 

7.  What  is  the  interest  of  $75  for  5  years,  at  3$? 

8.  What  is  the  interest  of  $120  for  8  years,  at  5  per 
cent.  ? 


INTEREST.  14-9 

9.  What  is  the  interest*  of  $100  for  10  years,  at  6 
per  cent.  ? 

10.  What  is  the  interest  of  $140  for  12  years,  at  5 
per  cent.  ? 

11.  What  is  the  interest  of  $150  for  5  years,  at  3 
per  cent.  ? 

12.  What  is  the  interest  of  $145  for  6  years,  at  5 
per  cent.  ? 

13.  What  is  the  interest  of  $200  for  10  years,  at  8 
per  cent.  ? 

14.  What  is  the  interest  of  $250  for  3  years,  at  8 
per  cent.  ? 

15.  What  is  the  interest  of  $220  for  11  years,  at  10 
per  cent.  ? 

1 6.  What  is  the  interest  of  $500  for  9  years,  at  8 
per  cent.  ? 

17.  What  is  the  interest  of  $250  for  12  years,  at  6 
per  cent.  ? 

1 8.  What  is  the  interest  of  $500  for  8  years,  at  12 
per  cent.  ? 

19.  What  is  the  interest  of  $200  for  9  years,  at  3 
per  cent.  ? 

20.  What  is  the  interest  of  $405  for  10  years,  at  8 
per  cent.  ? 

21.  What  is  the  interest  of  $50  for  2  years  and  2 
months,  at  6  per  cent.  ? 

ANALYSIS. — 2  months  is  ^  of  a  year.  2£  years  equals  J/ 
years.  If  the  interest  of  $1  for  1  year  is  6  cents,  for  J/ 
years  it  is  -1/  times  6  cents,  or  13  cents.  Therefore,  -jfc  of 
the  principal  equals  the  interest.  -^  of  $50  is  I-1/, 
or  $6.50,  the  interest. 

22.  What  is  the  interest  of  $25  for  4  years  and  3 
months,  at  4  per  cent.  ? 

23.  What  is  the  interest  of  $80  for  5  years  and  5 
months,  at  0  per  cent.  ? 

24.  What  is  the  interest  of  $60  for  8  years  and  6 
months,  at  6  per  cent.  ? 


150  INTEREST. 

25.  What  is  the  interest  of  $240  for  3  years  and  9 
months,  at  6  per  cent.  ? 

26.  What  is  the  interest  of  $75  for  4  years  and  8 
months,  at  9  per  cent.  ? 

27.  What  is  the  interest  of  $50  for  2  years  and  9 
months,  at  6  per  cent.  ? 

*8.  What  is  the  interest  of  $80  for  12  years  and  10 

months,  at  6  per  cent.  ? 
79.  What  is  the  interest  of  $69  for  8  years  and  4 

months,  at  2  per  cent.  ? 

30.  What  is  the  interest  of  $60  for  4  years  and  8 
months,  at  3  per  cent.  ? 

31.  What  is  the  interest  of  $600  for  2  years  4  months 
and  15  days,  at  4  per  cent.  ? 

ANALYSTS. — 15  days  is  \  of  a  month.  4£  months  equals 
|  months,  f  months  equals  •£%,  or  |  of  a  year.  2|  years 
equal  -^  years.  If  the  interest  of  $1  for  1  year  is  4  cents, 
for  ig§-  years  it  is  ^  times  4  cents,  or  -1/  cents.  Therefore, 
I^V  of  toe  principal  equals  the  interest.  ^  of  $600  is 
$57,  the  interest  required. 

32.  What  is  the  interest  of  $300  for  5  years  9  months 
and  18  days,  at  5  per  cent.  ? 

33.  What  is  the  interest  of  $550  for  4  years  7  months 
and  6  days,  at  10  per  cent.  ? 

34.  What  is  the  interest  of  $500  for  1  year  7  months 
and  18  days,-  at  6  per  cent.  ? 

35.  What  is  the  interest  of  $250  for  3  years  7"  months 
and  6  days,  as  4  per  cent.  ? 

36.  What  is  the  interest  of  $250  for  3  years  3  months 
and  6  days,  at  6  per  cent.  ? 

37.  What  is  the  interest  of  $50  for  6  years  4  months 
and  24  (Jays,  at  5  per  cent.  ? 

38.  What  is  the  interest  of  $75  for  2  years  11  months 
and  6  days,  at  15  per  cent.  ? 

39.  What  is  the  interest  of  $150  for  £  years  6  months 
and  12  days,  at  15  per  cent.  ? 

40.  What  is  the  interest  of  $300  for  2  years  9  months 
and  18  days,  at  1|  per  cent.  ? 


INTEREST.  151 

LESSON     LXY. 

1.  What  is  the  amount  of  $75  for  2  years,  at  6  per 
cent,  per  annum  ? 

ANALYSIS. —  If  the  interest  of  $1  for  1  year  is  6  cents, 
for  2  years  it  is  2  times  6  cents,  or  12  cents.  Therefore, 
Ti_3_,  or  /j,  of  the  principal  equals  the  interest.  /T  of  $75 
is  $9,  the  interest ;  to  which  add  $75,  the  principal,  and 
we  have  $84,  the  amount. 

2.  What  is  the  amount  of  $90  for  3  years,  at  7  per 
cent.  ? 

3.  What  is  the  amount  of  $100  for  4  years,  at  5  per 
cent.  ? 

4.  What  is  the  amount  of  $160  for  10  years,  at  5 
per  cent.  ? 

5.  What  is  the  amount  of  $160  for  8  years,  at  5  per 
cent.  ? 

6.  What  is  the  amount  of  $200  for  12  years,  at  5 
per  cent.  ? 

7.  What  is  the  amount  of  $210  for  2  years  and  6 
months,  at  4  per  cent.  ? 

8.  What  is  the  amount  of  $250  for  4  years  and  3 
months,  at  8  per  cent.  ? 

9.  What  is  the  amount  of  $240  for  4  years  and  2 
months,  at  3  per  cent.  ? 

10.  What  is  the  amount  of  $500  for  3  years  3  months 
and  6  days,  at  6  per  cent.  ? 

11.  What  is  the  amount  of  $200  for  5  years  4  months 
and  24  days,  at  5  per  cent.  ? 

LESSON     LXYI. 

i.  What  principal   will  in  4  years,   at  6  per  cent., 
give  $12  interest  ? 
ANALYSIS. —  If  the  interest  of  $1  for  1  year  is  6  cents,  for 


$2  ;  and  f  f ,  or  the  principal,  is  25  times  $2,  or  $50 


152 


INTEREST. 


2.  What  principal  will  in  6  years,  at  4  per  cent., 
give  $36  interest  ? 

3.  What  principal  will  in  4  years,  at  5  percent., 
give  $30  interest  ? 

4.  What  principal  will  in  8  years,  at  7  per  cent., 
give  $±2  interest  ? 

5.  What  principal  will  in  10  years,  at  7  per  cent., 
give  $140  interest  ? 

6.  What  principal  will  in  4  years  and  6  months,  at 
6  per  cent.,  give  $54  interest  ? 

7.  What  principal  will  in  4  years  and  3  months,  at 
5$,  give  $102  interest  ? 

8.  What  principal  will  in  4  years  and  3  months,  at 
8$,  give  $51  interest  ? 

9.  How  much  money  has  that  man  on  interest,  who, 
at  the  expiration  of  4  years  and  4  months,  at  6 
per  cent.,  receives  $260  interest  ? 

10.  At  the  expiration  of  2  years  and  4  months,  at  6 
per  cent.,  a  man   received  $49  interest.     How 
much  money  had  he  on  interest? 

11.  A.  is  worth  twice  as  much  as  B.,  and  the  interest 
of  their  united  fortunes  for  4  years  and  2  months, 
at  6$,  is  $600.     How  much  is  each  worth  ? 

12.  The  interest  on  the  cost  of  B.'s  store  and  house, 
for  1  year  and  6  months,  at  4%,  would  be  $270. 
What  was  the  cost  of  each,  provided  the  store 
cost  J  as  much  as  the  house  ? 

13.  If  the  money  B.  paid  for  a  sheep,  a  cow,  and 
a  horse,  was  put  on  interest  for  4  years  and  6 
months,  at  4  per  cent.,  it  would  give  $18  interest. 
What  was  the  cost  of  all,  and  of  each,  provided 
the  sheep  cost  J  as  much  as  the  cow,  and  the 
cow,  J  as  much  as  the  horse  1 

NOTE. — By  the  condition  of  the  question,  the  cow  must  have 
cost  3  times  as  much  as  the  sheep,  and  the  horse  2  times  as 
much  as  the  cow,  or  6  times  as  much  as  the  sheep. 


INTEREST.  153 


LESSON     LXYII. 

1.  What  principal  will  in  4  years,  at  5  per  cent., 
amount  to  $360  ? 

ANALYSIS. — If  the  interest  of  $1  for  1  year  is  5  cents,  for 
4  years  it  is  4  times  5  cents,  or  20  cents.  Therefore,  -^, 
or  |,  of  the  principal  equals  the  interest ;  to  which  add  f, 
the  principal,  and  we  have  f  of  the  principal  equal  to  the 
amount,  $380.  If  f  of  the  principal  is  $360,  |  of  the  prin- 
cipal is  £  of  $360,  which  is  $60,  and  f  (the  principal),  is  5 
times  $60,  which  is  $300. 

2.  "What  principal  will  in  3  years,  at  6  per  cent., 
amount  to  $118  ? 

3.  What  principal  will  in  6  years,  at  10  per  cent., 
amount  to  $120  ? 

4.  What  principal  will  in  10  years,  at  7  per  cent., 
amount  to  $170  ? 

5.  What  principal  will  in  4  years,  at  5  per  cent., 
amount  to  $660  ? 

6.  A.  is  worth  J  as  much  as  B. ;  and  the  interest  on 
their  united  fortunes  for  2  years,  at  5  per  cent.,  is 
$880.     What  is  the  fortune  of  each  ? 

7.  A  merchant  sold  a  quantity  of  cloth  for  $214, 
and  thereby  gained  7  per  cent. ;    what  did  the 
cloth  cost  him  ? 

8.  What  principal  will  in  2  years,  at  7  per  cent., 
amount  to  $1140  ? 

9.  What  principal  will  in  10  years  and  8  months,  at 
9  per  cent. ,  amount  to  $490  ? 

10.  The  amount  due  on  a  note,  which  had  been  on  in- 
terest 6  years  and  2  months,  at  6^,  was  $274; 
what  was  the  face  of  the  note  ? 

11.  What  principal  will  in  12  years  and  9  months,  at 
4%,  amount  to  $302  ? 

12.  If  -|-  of  A.'s  fortune  for  4  years  and  6  months,  at 
6$,  amounts  to  $127,  what  is  his  whole  fortune  ? 


154  INTEREST. 

r3«  If  |  of  B.'s  fortune,  being  put  on  interest  for  3 
years  3  months  and  6  days,  at  15  per  cent., 
amounted  to  $149,  what  was  his  whole  fortune  ? 

*4.  Mary,  being  asked  how  much  money  she  had  on 
interest,  and  at  what  per  cent.,  replied ;  .the  prin- 
cipal and  rate  %  are  such  that  in  5  years  the 
amount  would  be  $750,  and  in  7  years,  $810. 
What  was  the  principal  and  the  rate  per  cent.  ? 

15.  A  man  sold  two  horses  for  $240,  losing  on  the 
first   20  per  cent.,   gaining  on  the  other  20^ ; 
what  was  the  value  of  each  horse,  provided  he 
received  for  the  second  3  times  as  much  as  for 
the  first  \ 

1 6.  The   amount  of  Robert's  capital   for  a  certain 
time,  at  4$,  was  $360,  and  for  the  same  time, 
at  7$,  it  was  $405  ;  required  his  principal  and 
the  time. 


LESSON     LXYIII. 

r.  In  what  time  will  $40,  at  6  per  cent.j  give 
interest  ? 

ANALYSIS.— If  the  interest  of  $40  is  $12,  £f,  or  ^,  of  the 
principal  equals  the  interest.  If  the  interest  of  $1  for  1 
year  is  T3¥  of  a  dollar,  of  $100  it  is  100  times  $T3Tr,  or  $30. 
If  it  require  1  year  for  $100  to  give  $6  interest,  to  give  $30 
interest  it  will  require  as  many  years  as  $6  is  contained 
times  in  $30,  or  5  years. 

2.  In  what  time  will  $60,  at  5  per  cent.,  give  $18 
interest  \ 

3.  In  what  time  will  $90,  at  7  per  cent.,  give  $27 
interest  ? 

4.  In  what  time  will  $100,  at  6  per  cent.,  give  $10 
interest  ? 

5.  In  what  time  will  $120,  at  10  per  cent,  give  $120 
interest  ? 


PER     CENT.  155 

6.  In  what  time  will  $250,  at  6  per  cent.,  give  $20 
interest  ? 

7.  In  what  time  will  $iO,  at  7%,  give  $8.40  interest  \ 

8.  In  what  time,  at  8$,  will  $30  give  $9.60  interest  ? 

9.  In  what  time,  at  6$,  will  $10  give  $2.40  interest  ? 

10.  In  what  time,  at  4$,  will  $20  give  $5.60  interest  ? 


LESSON     LXIX. 

1.  At  what  rate  per  cent.,  will  $50,  in  1  year  and  6 

months  (or  1J  years),  give  $6  interest  ? 

ANALYSIS.— If  the  interest  of  $50  for  1£,  or  f  years,  is  $6, 
for  £  of  a  year  it  is  %  of  $6,  or  $2 ;  and  for  f ,  or  1  year,  it 
is  2  times  $2,  or  $4.  Therefore,  -fo,  or  -/-$,  of  the  principal 
equals  the  annual  interest.  Hence,  the  rate  per  cent,  is  /? 
of  100$  =  8$. 

2.  At  what  rate  per  cent.,  will  $40  annually  give  $2 
interest  3 

3.  At  what  rate  per  cent.,  will  $80  annually  give 
$3.20  interest  ? 

4.  At  what  rate  per  cent.,  will  $120  annually  give 
$12  interest  ? 

5.  At  what  rate  per  cent.,  will  $120  in  4  years,  give 
$20  interest  ? 

6.  At  what  rate  per  cent.,  will  $100  in  3  years,  give 
$30  interest  ? 

7.  At  what  rate  per  cent.,  will  $5  in  14  years,  give 
$7  interest  ? 

8.  At  what  rate  per  cent.,  will  $25  in  1  year  and  9 
months,  give  $3.50  interest  ? 

9.  At  what  rate  per  cent.,  will  $80  in  5  years  and  8 
months,  give  $34  interest  ? 

10.  At  what  rate  per  cent.,  will  $500  in  T  years  and 
6  months,  give  $15  interest  ? 

11.  At  what  rate  percent,  will  $600  in  2  years  4 
months  and  15  days,  give  $57  interest  I 


156  PEE     CENT. 


LESSON     LXX. 

1.  At   what   rate  per  cent.,  will  $10   in  4  years, 
amount  to  $12  ? 

REMARK. —  From  the  amount  subtract  the  principal, 
and  the  remainder  will  be  the  interest.  Then  proceed  as 
in  the  preceding  lesson. 

2.  At  what  rate  per  cent.,  will   $12   in   3  years, 
amount  to  $13.44? 

3.  At  what  rate  per  cent.,  will   $20  in  6  years, 
amount  to  $26  ? 

4.  At   what  rate  per  cent.,  will  $24  in  10  years, 
amount  to  $3B  ? 

5.  At   what  rate  per  cent.,  will  $30   in  7  years, 
amount  to  $36.30  ? 

6.  At  what  rate  per  cent,,  will  $50  in  10  years, 
amount  to  $75  ? 

7.  At   what   rate  per  cent.,  will   $36   in  5  years, 
amount  to  $39.60  ? 

8.  At  what  rate  per  cent.,  will  the  interest  for  20 
years  equal  a  given  principal  ? 

ANALYSIS. — With  the  interest  at  100$,  it  would  equal 
a  given  principal,  or  a  given  principal  will  double  itself 
in  1  year,  at  100  per  cent. ;  and  in  20  years,  at  ^  of  100 
per  cent.,  or  5  per  cent. 

9.  At  what  rate  per  cent.,  will  a  given  principal 
double  itself,  in  4  years  ? 

10.  At  what  rate  per  cent.,  will  a  given  principal 
double  itself,  in  3  years  ? 

11.  At  what  rate  per  cent,,  will  the  interest  equal  a 
given  principal  in  5  years  ? 

12.  At  what  rate  per  cent.,  will  $80  in  7  years  give 
$80  interest  ? 

13.  At  what  rate  per  cent.,  will  $640  in  6  years  give 
$640  interest  ? 


PER      CENT.  157 

14.  At  what  rate  per  cent.,  will  25  cents  in  8  years 
give  25  cents  interest  ? 

15.  At  what  rate  per  cent.,  will  $97  in  9  years  give 
$97  interest  ? 

1 6.  At  what  rate  per  cent.,  will  $372  in  25  years 
give  $372  interest  ? 

17.  At  what  rate  per  cent.,  will  $1  in  30  years  give 
$1  interest? 

1 8.  -At  what  rate  per  cent.,  will  $15  in  12J  years 

give  $15  interest  ? 

19.  At  what  rate  per  cent.,  will  $12  in  llf  years 
give  $12  interest  '\ 

20.  At  what  rate  per  cent.,  will  5  cents  in  16|  years 
give  5  cents  interest  I 


LESSON     LXXI. 

1.  In  what  time  will  a  given  principal  double  itself, 
at  5  per  cent.  ? 

ANALYSIS. — A  given  principal  will  double  itself  in  100 
years,  at  1  per  cent,  and  at  5  per  cent.,  in  £  of  100 
years,  which  is  20  years. 

2.  In  what  time  will  a  given  principal  double  itself, 
at  4  per  cent.  ? 

3.  In  what  time  will  $25,  at  3  per  cent.,  give  $25 
interest  ? 

4.  In  what  time  will  $275,  at  6  per  cent.,  give  $275 
interest  ? 

5.  Jn  what  time  will  the  interest  equal  a  given  prin- 
cipal, at  2  per  cent.  ? 

6.  In  what  time  will  $1,  at  7$,  give  $1  interest  ? 

7.  In  what  time  will  $94,  at  9$,  give  $91  interest  ? 

8.  In  what  time  will  5  cents,  at  8  per  cent.,  give  5 
cents  interest  ? 


158  PEK     CENT. 

9.  In  what  time  will  $3f ,  at  10  per  cent.,  give 

interest  ? 

10.  In  what  time  will  1  dime,  at  12  J  per  cent.,  give 
1  dime  interest  ? 


LESSON     LXXII. 

1.  Bought  a  bushel  of  grass-seed  for  $5,  and  sold  it 
for  $7 ;  what  was  the  gain  per  cent.  ? 

ANALYSIS. — Since  it  was  bought  for  $5,  and  sold  for 
$7,  the  gain  was  $7— $5,  which  is  $2.  Therefore,  f  of  the 
cost  equals  the  gain.  Hence,  the  gain  per  cent,  was  £  of 
100  per  cent.,  which  is  40  per  cent. 

2.  A  book  was  bought  for  $2,  and  sold  for  $3 ;  what 
was  the  gain  per  cent.  ? 

3.  A  shawl  cost  $5,  and  was  sold  for  $8 ;  what  was 
the  gain  per  cent.  ? 

4.  A  cow  was  bought   for  $20,  and  sold  for  $25 ; 
what  was  the  gain  per  cent.  ? 

5.  A  merchant  bought  a  hogshead  of  molasses  for 
$80,  and  sold  it  for  $95 ;  what  did  he  gain  per 
cent.  ? 

6.  A  barrel  of  pork  cost  $12,  and  was  sold  for  $11 ; 
what  was  the  loss  per  cent.  ? 

7.  A  horse  was  bought  for  $140,  and  sold  for  $60 ; 
what  was  the  loss  per  cent.  ? 

8.  Bought  an  orange  for  4  cents,  and  sold  it  for  6 
cents ;  wrhat  was  the  gain  per  cent.  ? 

9.  Bought  a  melon  for  15  cents,  and  sold  it  for  20 
cents ;  what  was  the  gain  per  cent.  ? 

jo.  Bought  a  book   for  5  dimes,  and  sold  it  for  8 
dimes ;  what  was  the  gain  per  cent.  ? 

1 1.  Bought  a  hectometre  of  silk  for  $120,  and  sold  it 
for  $200 ;  what  was  the  gain  per  cent.  ? 

12.  A  boy  sold  melons,  at  the  rate  of  10  cents  each 


PERCENTAGE.  159 

\  of  which  equaled  his  gain ;  how  much  would 
he  have  gained  per  cent.,  if  he  had  sold  them  at 
1 2  cents  each  ? 

13.  A  merchant  sold  sugar  for  $80  a  hogshead,  and 
thereby  cleared  ^  of  this  money ;  if  he  had  sold 
it  at  $92  a  hogshead,  what  would  he  have  gained 
per  cent.  ? 

14.  A  quantity  of  cloth  was  bought  for  $36,  and  sold 
for  $43  ;  what  was  the  gain  per  cent.  ? 

15.  A  horse  was  bought  for^$100,  and  sold  for  $95  ; 
what  was  the  loss  per  cent.  ? 

1 6.  A  man  re-sold  a  kilogramme  of  wheat  for  $120, 
and  cleared  -J  of  its  cost ;  how  much  money  would 
he  have  lost  per  cent.,  if  he  had  sold  it  for  $80  ? 

1 7.  What  per  cent,  of  £  is  1  ?    Of  f  is  J  ?    Of  f  is  ^  ? 
Of  f  is  |?    Of  J  is  11     Of2JiB-§?    Of3£is 
2-V? 

1 8.  §  of  $6  is  what  per  cent,  of  |  of  $100  ? 

19.  |  of  $28  is  |  of  what  percent,  of  f  of  $300  ? 

20.  Walter  sold  a  horse  for  $120,  and  thereby  gained 

of  its  cost ;  what  would  he  have  lost  per  cent. 
>y  selling  it  for  $80  ? 


LESSON     LXXIII. 

1.  A  man  bought  a  cow  for  $20;  for  what  must  he 
sell  her,  to  gain  5  per  cent.  ? 

ANALYSIS.— If  he  gain  5  per  cent.,  he  gains  Tfj,  or  ^  of 
the  cost.  2^  of  $20  is  $1,  the  gain.  Therefore,  to  gain  5 
per  cent.,  he  must  sell  the  cow  for  $20  +  $1,  or  $21. 

2.  A  man  bought  a  yoke  of  oxen  for  $100 ;  how 
must  he  sell  them,  to  gain  6  per  cent.  ? 

3.  A  man  bought  a  barrel  of  flour  for  $10 ;  for  what 

must  he  sell  it,  to  gain  10  per  cent.  ? 


160  DISCOUNT. 

4.  A  gallon  of  wine  was  bought  for  20  dimes  ;  how 
must  it  be  sold  a  pint,  to  gain  20  per  cent.  ? 

5.  A  hogshead  of  molasses  cost  $20;  for  what  ought 
it  to  be  sold  a  gallon,  to  gain  40  per  cent.  ? 

6.  B.  bought  a  horse  for  $80,  and  by  selling  it,  lost 
5  per  cent. ;  for  what  did  he  sell  'it  ? 

7.  A  wagon  cost  $140,  and  was  sold  at  a  loss  of  5 
per  cent. ;  for  what  was  it  sold  ? 

8.  A  merchant,  by  selling  40  metres  of  cloth  for 
$164,  lost  20  per  cent. ;    what  did  it  cost  per 
metre  ? 

9.  If  3  decalitres  and  5  litres  of  wine  cost  $140, 
how  must  it  sell  per  litre  to  gain  20^  ? 

10.  B.  lost  5  per  cent,  by  selling  a  hectolitre  of  rum, 
which  cost  $80 ;  for 'what  did  he  sell  it  a  litre  ? 


LESSOJST     LXXIY. 

1.  What  principal  wilt,  in  4  years,  at  5  per  cent., 
amount  to  $60  ? 

ANALYSIS. — If  the  interest  of  $1  for  1  year  is  5  cents,  for 
4  years  it  is  4  times  5  cents,  or  20  cents.  "Therefore,  -£fa,  or 
£  of  the  principal  equals  the  interest ;  to  which  add  | ,  the 
principal,  and  we  have  £  of  the  principal  equal  to  the 
amount,  or  $60.  Iff  of  the  principal  is  $60,  -^  of  the  prin- 
cipal is  %  of  $60,  which  is  $10 ;  and  £  (the  principal),  is  5 
times  $10,  which  are  $50. 

2.  What  principal  will,  in  3  years,  at  6  per  cent., 
amount  to  $118  ? 

3.  What   principal  will,  in  5  years,  at  6  per  cent., 
amount  to  $130  ? 

4.  What  principal  will,  in  7  years,  at  5  per  cent., 
amount  to  $81  ? 

5.  What   principal  will,  in  9  years,  at  8  per  cent., 
amount  to  $86  ? 

6.  What  principal  will,  in  3|  years,  at  8  per  cent., 
amount  to  $260  ? 


DISCOUNT.  161 

7.  What  principal  will,  in  4-f  years,  at  6  per  cent., 
amount  to  $640  ? 

8.  AVliat  principal  will,  in  5f  years,  at  7  per  cent., 
amount  to  $42  ?  f 

9.  What  principal  will,  in  6f  years,  at  7  per  cent., 
amount  to  $87  ? 

10.  What  principal  will,  in  8-f  years,  at  6  per  cent., 
amount  to  $76  ? 

The  present  ivorth  of  a  debt  payable  at  some  fu- 
ture time,  without  interest,  is  such  a  sum  as  will,  in  the 
given  time,  and  at  the  given  rate  per  cent.,  amount  to  the 
debt.  Hence,  the  present  worth  of  any  sum  of  money,  pay- 
able at  some  future  time  without  interest,  may  be  found 
in  the  same  way  that  we  found  the  principal,  when  the 
amount,  time,  and  rate  per  cent,  were  given. 

See  the  Analysis  of  this  Lesson. 

11.  What  is  the  present  worth  of  $26,  due  5  years 
hence,  at  6  per  cent.  ?  Ans.  $20. 

12.  What  is  the  present  worth  of  $14,  due  8  years 
hence,  at  5  per  cent.  ? 

13.  What  is  the  present  worth  of  $110,  due  5  years 
hence,  at  5  per  cent.  ? 

14.  What  is  the  present  worth  of  $86,  due  8  years 
hence,  at  9  per  cent. '? 

15.  What  is  the  present  worth  of  $102,  due  9  years 
hence,  at  4  per  cent.  ? 

1 6.  What  is  the  present  worth  of  $72,  dne  4  years 
hence,  at  5  per  cent.  ? 

Discount  equals  the  amount  minus  the  present  worth. 

17.  What  is  the  discount  on  $46,  due  3  years  hence, 
at  5  per  cent.  ? 

1 8.  What  is  the  discount  on  $54,  due  5  years  hence, 
at  7  per  cent.  ? 

19.  What  is  the  discount  on  $65,  due  5  years  hence, 
at  6  per  cent.  ? 

20.  What  is  the  discount  on  $93,  due  3  years  hence, 
at  8  per  cent.  3 


162  PERCENTAGE. 

21.  What  is  the  present  worth  of  $186,  due  4|  years 
hence,  at  5  per  cent.  ? 

22.  What  is  the  present  worth  of  $66,  due  5J  years 
hence,  at  6  per  cent.  ? 

23.  What  is  the  present  worth  of  $128,  due  4|  years 
hence,  at  6  per  cent.  ? 


LESSON     LXXV. 

1.  If  I  sell  cloth  at  $2.50  a  yard,  and  thereby  gain 
25  per  cent.,  what  did  it  cost  a  yard  ? 

ANALYSIS. —  If  I  gain  25  per  cent.,  I  gain  |-  of  the  cost ; 
to  which  add  £,  the  cost,  and  I  have  f-  of  the  cost  equal  to 
$2.50.  If  £  of  the  cost  is  $2.50,  -\  of  the  cost  is  £  of  $2.50, 
or  50  cents ;  and  |-  (the  cost)  is  4  times  50  cents,  which  are 
200  cents,  or  $2. 

2.  A  horse  was  sold  for  $38,  which  was  at  a  loss  of 
5$ ;  what  did  the  horse  cost  ? 

3.  If  I  sell  cloth  at  $2.50  a  yard,  and  thereby  gain 
25$,  how  must  I  sell  it  a  yard  to  lose  20$  ? 

4.  If  I  sell  cloth  at  $4.40  a  metre,  and  thereby  gain 
10$,  how  ought  I  sell  it  to  lose  25$  ? 

5.  If  by  selling  a  piece  of  cloth  for  §46,  I  gain  15$, 
how  ought  I  to  have  sold  it,  to  have  lost  30$  ? 

6.  A.  sold  his  horse  for  $105,  and  thereby  gained  5$ ; 
for  what  ought  he  to  have  sold  it,  to  have  lost  10$  1 

7.  A  farm  was  sold  for  $495,  which  was  10$  less 
than  what  it  was  worth  ;  for  what  ought  it  to  have 
been  sold,  to  have  received  40$  more  than  its 
value  ? 

8    A  mechanic  lost  20$  on  the  cost  of  a  wagon,  by 

selling  it  for  $10 ;  for  what  ought  it  to  have  been 

sold,  to  have  gained  30  per  cent.  ? 
9.  A  hectare  was  sold  for  $90,  which  was  10$  less 

than  its  value ;  what  would  have  been  the  gain  per 

cent.,  if  it  had  been  sold  for  $120  ? 


PERCENTAGE.  163 

10.  A  farm  was  sold  for  $690,  which  was  8$  ]ess 
than  its  value ;  what  would  have  been  the  gain 
%  on  its  value,  if  it  had  been  sold  for  $850  ? 

jj.  A  book  was  sold  for  90  cents,  which  was  10$ 
less  than  its  value ;  what  would  have  been  the 
gain  %  on  its  value,  if  it  had  been  sold  for  $1.50  ? 

12.  A  man  sold  two  watches,  at  $12  each;  on  one 
he  gained  50$,  and  on  the  other  he   lost   50$. 
Did  he  gain  or  lose  by  the  bargain,  and  how 
much  ? 

13.  An  individual  sold  two  gold  pencils,  at  $6  each; 
on  one  he  gained  20$,  and  on  the  other  he  lost 
20$.     Did  he  gain  or  lose,  and  how  much  ? 

14.  A  farmer  sold  two  horses  at  $210  each;  for  one 
he  received  25$  more  than  its  value,  and  for  the 
other  25%  less  than  its  value.     Did  he  gain  or 
lose  by  the  sale  of  both,  and  how  much  ? 

15.  A  merchant  sold  a  quantity  of  cloth  for  $280, 
and  by  so  doing  lost  60$ ;  he  then  sold  another 

'  quantity  for  $80,  and  gained  60$.     Did  he  gain 
or  lose  by  the  entire  sale,  and  how  much  ? 


LESSON     LXXYI. 

1.  An  individual  was  ordered  to   collect   $190,  and 
his  own  fee,  which  was  to  be  5  per  cent,  on  all  the 
money  collected.     How  much  should  be  receive  ? 

ANALYSIS. — He  is  to  receive  5  per  cent.,  or  y|y ,  or  ¥1¥  of 
all  he  collects.  f£,  all  he  collects,  minus  F1^  n*s  fee,  equals 
£$  of  all  he  collects,  or  $190,  the  amount  he  is  to  pay  his 
employer.  If  -||  of  what  he  collects  equals  $190,  ^  is  -fa 
of  $190,  which  is  $10  ;  and  f-£  (what  he  collects)  is  20  times 
$10,  or  $200.  Therefore  he  must  receive  $200— $100= $10. 

2.  How  much  ought  A.  to  receive  for  collecting  $90 
and  his  own  fee  of  10  per  cent,  on  all  he  collect?  ^ 


164  MISCELLANEOUS     QUESTIONS. 

3.  What  amount  of  money  will  be  sufficient  to  pay  a 
debt  of  $38  and  the  collector's  fee,  which  is  5  per 
cent,  on  all  the  money  collected  ? 

4.  How  much  cider  must  that  man  make  to  bring 
away  15  barrels,  after  the  owner  of  the  mill  re- 
ceives 1B|  per  cent,  of  all  he  has  made  ? 

5.  How  much  grain  must  a  farmer  take  to  mill,  that 
he  may  bring  away  the  flour  of  1  bushel,  after  the 
miller  has  taken  10  per  cent,  of  all  he  took  there  \ 


MISCELLANEOUS    QUESTIONS. 

1.  At  5  p'er  cent,  for  4  years,  what  part  of  the  prin- 
cipal equals  the  interest  ? 

2.  In  how  many  years,  at  4  per  cent.,  will  the  in- 
terest on  a  given  principal  amount  to  the  same 
sum,  as  it  will  in  8  years,  at  6  per  cent.  ? 

3.  At  what  rate  per  cent,  will  the  interest  on  a  given 
principal,  in  14  years,  amount  to  the  same  sum, 
as  it  will  in  12  years  at  Y  per  cent.  ? 

4.  If  -fa  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent.  ? 

5.  The  rent  of  B.'s  farm,  for  8  years,  equaled  jj$ 
of  its  value ;  what  per  cent,  did  he  annually  re- 
ceive on  the  value  of  his  farm  ? 

6.  What  is  the  interest  of  $75,  for  5-|  years,  at  6  per 
cent.  ? 

7.  What  principal  will,  in  7|  years,  at  8  per  cent., 
give  $2±  interest  ? 

8.  What  principal  will,  in  4f  years,  at  5  per  cent., 
amount  to  $155  ? 

9.  At  what  rate  per  cent,  will  a  given  principal  double 
itself  in  12^  years? 

10.  The  interest  of  A.'s  and  B.'s  fortune,  for  8  years. ; 
at  5  per  cent.,  is  $420 ;   what  is  the  fortune  o 
each,  provided  A.'s  fortune  is  twice  B.'s  ? 


MISCELLANEOUS     QUESTIONS.  165 

IT.  The  interest  of  f  of  A.'s  and  f  of  B.'s  fortune, 
for  7  years,  at  5  per  cent.,  is  $2100 ;  what  is  each 
of  their  fortunes,  provided  f  of  A.'s  fortune  equals 
|  of  B.'s? 

1 2.  B.  sold  his  horse  for  \  of  1 J  times  what  it  cost ; 
what  did  he  lose  per  cent.  ? 

13.  What  is  the  interest  of  $540  for  4  years,  at  5  per 
cent,  ? 

14.  What  is  the  interest  of  $180,  for  5  years  and  9 
months,  at  6f  per  cent.  ? 

15.  What  principal  will  in  4  years  7  months  and  6 
days,  at  6|  per  cent.,  amount  to  $412  ? 

1 6.  The  interest  of  the  cost  of  B.'s  horse,  sleigh,  and 
wagon,  for  6  years,  at  5  per  cent,,  is  $69.     What 
is  the  cost  of  each,  provided  their  prices  are  to 
each  other  as  ^-,  f ,  an$  |  ? 

17.  What  principal  will,  in  8  years  and  8  months,  at 
7f  per  cent.,  amount  to  $419  3 

1 8.  What  principal  will,  in  5  years  9  months  and  18 
days,  at  10  per  cent.,  give  $116  interest  \ 

19.  In  what  time  will  $420,  at  5  per  cent.,  give  $147 
interest  ? 

20.  If  the  interest  of  $200,  for  1  year  and  6  months, 
is  $18,  what  is  the  rate  per  cent.  ? 

21.  At  what  rate  per  cent,  will  $500,  in  4  years  and 
9  months,  give  $190  interest  ? 

22.  At  what  rate  per  cent.,  will  $500,  in  22  years 
and  6  days,  amount  to  $1821  ? 

23.  At  what  rate  per  cent,  will  a  given  principal 
double  itself,  in  20  years? 

24.  In  what  time  will  the  amount  be  double  a  given 
principal,  at  12 \  per  cent.  ? 

25.  At  what  rate  per  cent,  will  the  amount  be  double 
a  given  principal,  in  6  years  and  8  months  ? 

26.  A  horse  was  bought  for  $60,  and  sold  for  $90; 
what  was  the  gain  per  cent.  \ 


106  MISCELLANEOUS     Q  U  E  8  T  I  O  N  S  . 

27.  A  basket  containing  39  oranges,  cost  $1.20 ;  Low 
must  they  be  sold  each  to  gain  30  per  cent."? 

28.  If  1  litre  of  wine  cost  40  cents,  how  must  it  be 
sold  a  decilitre  to  gain  20  per  cent.  ? 

29.  What  is  the  present  worth  of  $68,  due  10  years 
hence,  at  7  per  cent.  ? 

30.  What  is  the  discount  on  $162,  due  10  years  and 
4  months  hence,  at  6  per  cent.  ? 

31.  What  is  the  present  worth  of  $87,  due  3J  years 
hence,  at  5  per  cent.  ? 

32.  If  a  hogshead  of  molasses  containing  84  gallons 
cost  $30,  how  must  it  be  sold  a  gallon,  to  gain 
40  per  cent.  ?  „ 

33.  The  money  I  have  on  interest,  in  9  years,  at  10 
per  cent.,  amounts  to  $190  ;  what  is  the  principal  ? 

34.  When  money  was  worth  6  per  cent,,  I  bought 
$400  worth  of  goods ;    6  months  afterwards  I 
sold  them,  and  gained  10  per  cent,  on  the  cost. 
How  much  did  I  gain  ?  Ans.  $28. 

35.  A  speculator  bought  a  horse  for  $36,  and  sold  it 
for  25  per  cent,  more  than  he  gave  for  it ;  which, 
however,  was  10  per  cent,  less  than  what  he  asked 
for  it.     How  much  did  he  ask  for  the  horse  ? 

36.  A  gentleman  being  asked  how  much  money  he 
hacl  on  interest,  replied,  that  if  instead  of  6  per 
.cent,  he  should  receive  10  per  cent.,  he  would  re- 
ceive $268  interest  more  than  he  then  did.    How 
much  money  had  he  on  interest  ? 

37.  A  merchant  bought  broadcloth  for  $1.20  a  yard, 
and  sold  it  for  33J  per  cent,  more  than  he  gave 
for  it ;   which,  however,  was  33-J  per  cent,  less 
than  his  marked  price  for  it.    How  much  was  his 
marked  price  per  yard  ? 

38.  A   Frenchman   sold  a  hectometre  of  cloth   for 
$120,  and  gained  50  per  cent.     He  sold  another 
hectometre  for  $120,  and  lost  50  per  cent.     Did 
he  gain  or  lose  by  both  sales  ?   how  much  ? 


MISCELLANEOUS     QUESTIONS.  167 

39.  B.  sold  a  horse  for  $60,  and  gained  20  per  cent, 
He  then  sold  another  horse  for  $60,  and  lost  60 
per  cent.     Did  he  gain  or  lose,  and  how  much  ? 

40.  The  interest  on  1J  times  A.'s,  and  |  of  B.'s  for- 
tune, for  8  years,  at  5  per  cent.,  is  $520.     What 
is  the  fortune  of  each,  provided  1J  times  A.'s  for- 
tune equals  f  of  B.'s  \ 

41.  |  of  D.'s  fortune  added  to  f  of  E.'s,  which  is  3 
times  |  of  D.'s,  being  on  interest  for  8  years,  at  5 
per  cent.,   gives    $800   interest.      What   is   the 
fortune  of  each  ? 

42.  The  interest  on  A.'s,  B.'s  and  C.'s  fortunes,  for  6 
years,  at  8  per  cent.,  is  $1040.     What  is  the  for- 
tune of  each,  provided  they  are  to  each  other  as 


43.  The  interest  of  A.'s,  B.'s,  and  C.'s  fortunes,  foi 
5J  years,  at  6  per  cent.,  is  $800.     What  is  each 
of  their  fortunes,  provided  B.'s  is  twice  A.'s,  and 
B.'s  and  C.'s  are  equal  ? 

44.  A.'s  fortune  added  to  f  of  B.'s,  which  is  to  A.'B 
as  2  is  to  3,  being  put  on  interest  for  6  years,  at 
4  per  cent.,  amounts  to  $124.     What  is  the  for- 
tune of  each  ? 

45.  D.'s  money  added  to  4  times  E.'s,  which  is  equal 
to  D.'s,  being  on  interest  for  10  years,  at  5  per 
cent.,  amounted  to  $3000.     What  was  each  of 
their  fortunes  ? 

46.  The  sum  of  f  of  A.'s  and  \  of  B.'s  money,  being 
on  interest  for  8  years,  at  5  per  cent.,  amounts  to 
$2100.     Provided  \  of  B.'s  money  is  twice  §  of 
A.'s,  how  much  money  has  each  ? 

47.  f  of  the  cost  of  C.'s  house,  increased  by  f  of  the 
cost  of  his  farm,  being  placed  on  interest  for  10 
years,  at  7  per  cent.,  amounts  to  $17000.     What 
is  the  cost  of  each,  if  f  of  the  cost  of  the  house  is 
only  -^  of  |  of  the  cost  of  the  farm  ? 

48.  If  f  of  A.'s  fortune  in  2  years  and  4  months,  at  6 


168  MISCELLANEOUS     QUESTIONS. 

per  cent.,  amounts  to  $570,  what  is  bis  whole 
fortune  ? 

49.  The  sum  of  A.'s  and  B.'s  fortunes,  in  4  years  and 
8  months,  at  6  per  cent.,  amounted  to  $'256.  What 
was  each  of  their  fortunes,  provided  f  of  A.'s  for- 
tune equaled  B.'s  ? 

50.  The  interest  for  5  years,  at  6  per  cent.,  on  f  of 
the  money  Morgan  owes  is  $180  ;  and  the  inter- 
est for  the  same  time  and  rate  per  cent.,  on  f  of 
the  money  due  him,  is  $120.     How  much  has 
Morgan  after  paying  his  debts  't 

51.  The  money  John  paid  for  a  sheep,  a  cow,  and  a 
horse,  in  8  years,  at  10  per  cent.,  would  give  such 
an  interest,  as  would  in  |  as  long,  at  \  as  great  a 
per  cent.,  amount  to  $104 ;  how  much  did  he  pay 
for  each,  provided  the  sheep  cost  \  as  much  as 
the  cow,  and  the  cow  J  as  much  as  the  horse '? 

52.  The  interest  of  the  sum  of  |  of  Simpson's,  -|  of 
Eyer's,  and  -f^  of  Domer's  fortunes,  for  3  years 
7  months  and  6  days,  at  10  per  cent.,  is  such  as 
will  in  the   same  time,  at  \  the  rate  per  cent , 
amount  to  $531.     What  is  the  fortune  of  each, 
provided  l|  times  Domer's  part  of  the  principal 
equals  f  of  Eyer's,  and  -f$  of  Eyer's  part  of  the 
principal  equals  J  of  Simpson's  ? 

53.  The  interest  of  the  sum  of  |-  of  A.'s,  and  f  of 
B.'s  fortune,  for  a  certain  time,  at  2  per  cent., 
was  to  this  sum  as  9  to  250.     And  the  amount 
of  this  interest  for  25  times  as  long,  at  10  times 
as  great  a  per  cent.,  was  $180.     What  was  each 
of  their  fortunes,  provided  A.'s  fortune  was  to  B.'s 
as  1  to  3  ?   And  how  long  was  the  first  on  interest  ? 

EEMAEK. —  Since  the  interest  was  to  the  principal  as  9  to 
250,  ^fg.  of  the  principal  equals  the  interest.  Hence,  1  year 
9  months  and  18  days  is  the  time  required,  &c. 


NUMERATION     AND     DECIMALS.  109 


NUMERATION  AND   DECIMALS. 

In  view  of  the  importance  and  utility  of  the  Decimal  system 
of  Weights,  Measures,  and  Currency,  the  Notation  of  our 
Decimal  Arithmetic,  including  Decimal  Fractions,  is  now  pre- 
sented, that  pupils  may  comprehend  the  simplicity  of  the  sys- 
tem, and  more  easily  perform  calculations  on  the  Tables. 

The  Decimal  System  of  Measures  and  Weights  having  the 
Metre,  the  Litre,  and  the  Gram  as  principal  units,  and  of 
currency  having  the  Dollar  as  the  principal  unit  in  the  United 
States,  Canada,  and  some  other  countries,  and  the  Franc  as  the 
principal  unit  in  France,  will  be  found  simple  and  useful  to 
insure  accuracy  of  computation  and  economy  of  time. 

The  denominations  are  also  systematic.  For  those  greater 
than  the  principal  unit,  prefixes  from  the  Greek  language  are 
used,  as  follows :  deka  (from  deka,  ten)  ;  Jiedo  (from  ekaton,  hun- 
dred) ;  kilo  (from  kilion,  thousand) ;  and  myria  (from  murias, 
ten  thousand).  For  denominations  less  than  the  principal  unit, 
prefixes  from  the  Latin  language  are  used,  as  follows :  deci 
(from  decem,  ten)  ;  centi  (from  centum,  hundred) ;  milli  (from 
mille,  thousand),  etc.  Therefore,  1  decimetre  is  equal  to  one 
tenth  part  of  a  metre,  and  1  decametre  is  ten  metres.  See 
Tables  on  pages  55,  56. 

Figures  express  numbers  and  parts  of  numbers. 

A  Wiiole  Number  is  called  an  Integral  Number, 
and  the  figures  expressing  it  are  named  Integer's; 
as,  1,  8,  25. 

A  Part  of  a  Number  is  called  a  Fractional  Num- 
ber, and  the  figures  expressing  it  are  named  Frac- 
tions; as,  J,  \\,  .2,  or  ^ 

The  whole  number  of  which  the  fraction  is  a  part, 
is  called  the  unit  of  the  fraction. 

A  Common  Fraction  is  one  or  more  of  the  equal 
parts  of  any  quantity,  and  is  expressed  by  two  terms, 
the  Numerator  and  Denominator,  with  a  line  between 
them,  as  J,  §  of  a  yard,  4  of  10. 

A  Decimal  Fraction  is  a  division  of  a  unit  into 
tenths,  etc.,  according  to  the  scale  of  the  Numeration 

8 


170  N  U  M  E  K  A  T  I  O  N     AND     DECIMALS. 

Table,  and  is  expressed  by  its  numerator  only,  having 
a  dot  ( . ),  called  a  decimal  point,  before  it ;  thus, 
.1  A>  .23  =  J^. 

A  Mixed  Number  is  a  number  expressed  by  an 
Integer  and  a  Fraction  ;  as,  3  j,  20f . 

A  Mixed  Fraction  is  a  decimal  and  common  frac- 
tion united  in  one ;  thus,  .3  J  is  read  three  and  one 
half  tenths. 

An  Abstract  Number  is  a  number  that  expresses 
no  particular  kind  of  quantity  ;  or  number  considered 
without  denominative  quantity;  as  2,  19,  7J. 

A  Denominate  Number  is  a  number  used  in  con- 
nection with  a  name  of  quantity;  as,  4  yards,  8-J 
bushels,  $24,  40  metres. 

In  the  Decimal  System  of  Notation,  ten  charac- 
ters, or  figures,  are  used,  viz.,  the  nine  significant 
figures,  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  the  cipher,  0. 

Each  figure  may  have  two  values,  one  when  it  is 
alone,  which  is  its  simple  value;  the  other  when  it 
is  used  with  other  figures,  which  is  its  local  value : 
thus,  1  represents  one,  or  a  unit ;  4  represents  four, 
or  four  units. 

If  these  two  figures  are  put  together,  one  changes 
its  value ;  thus,  14  represents  fourteen,  or  one  ten 
and  four  units ;  and  41  represents  forty-one,  or  four 
tens  and  one  unit. 

If  another  figure  be  added  on  the  right,  both  of 
the  two  figures  change  in  value  ten-fold  ;  thus,  142 
signifies  one  hundred  and  forty-two;  and  410  is  four 
hundreds  one  ten  and  no  units,  or  four  hundred  and 
ten. 

If  another  figure  be  added  on  the  left,  it  represents 
its  proper  local  value,  but  does  not  affect  the  figures 
to  which  it  is  thus  added,  because  it  has  not  changed 
their  places ;  thus,  3142  represents  three  thousands, 
one  hundred,  four  tens,  and  two  units,  or  is  read, 
three  thousand  one  hundred  and  forty-two. 


NUMERATION     OF     I  N  T  E  G  E  JLi  B  .  171 

The  place  of  a  figure  denotes  its  value,  according 
to  the  scale  of  the 


I  NUMERATION    TABLE. 

I    «         If 

S      §  5      5      «5      _: 


2  Two. 

*    2  3  Twenty-three. 

235  Two  hundred  thirty-five. 

2354:  Two  thousand  three  hundred  fifty-four. 

23546  Twenty -three  thousand  five  hundred  forty-six. 

"     *     *     "2354:60      Two  hundred  thirty-five  thousand  four  hundred  sixty. 

•  .     »OQ£/LAnft      Tvro  millions  three  hundred  fifty-four  thousand  fcix  hun- 

&  O  O   tt   D   U   O          dred  and  eight. 

•  •OQK/lfifiQ~l       Twenty-three  millions  five  hundred  forty-six  thousand 

JOO*OU01          and  eighty-one. 

•  OQJ^zL^Afil    Q      Two   hundred   thirty-five  million    four  hundred  sixty 
^OO^bOUOlJ          thousand  eight  hundred  and  nineteen. 

20    K    A    {$   A    Q    1    Q'Z      Two  billions  three  hundred  fifty-four  millions  six  him- 
OUT     JUOJ-i/     1          dred  and  eight  thousand  one  hundred  ninety-seven. 

NOTE. — These  denominations  are  sometimes  divided  into 
periods  of  three  each  from  the  right,  the  first  period  being  of 
units,  the  second  being  of  thousands,  the  third  being  of  mil- 
lions, the  fourth  being  of  billions,  the  fifth  being  of  trillions, 
the  sixth  being  of  quadrillions,  etc. 

A  figure  being  moved  one  place  to  the  left,  in  the 
above  table,  increases  its  value  ten-fold,  and  ten  of 
one  place  equal  one  of  the  next  place  on  its  left. 

Although  a  cipher  expresses  no  number,  it  is  used 
to  locate  figures  of  other  orders  in  their  proper 
places ;  thus,  to  express  six  thousand  and  eighty-one 
(6081),  the  cipher  locates  the  figure  6  in  its  proper 
place. 

Read  the  following  numbers  : 

302  —  4516  —  2007  — 180960  —  81108  —  9716439 
- 17647  —  2854  —  430000  —  5000006  —  340657  — 
9977700  — 18001800  —  24697  —  684321  —  5402835. 


172  NOTATION     OF     DECIMALS. 

The  Notation  of  Decimal  Fractions  or  Decimals, 
is  in  harmony  with  that  of  Integers,  as  shown  in  the 


following 


TABLE   OF   INTEGEKS    AND    DECIMALS. 


INTEGERS. 

Two  tenths, 

Twenty-three  hundredths,  .23*     *     "  * 

Two  hundred  and  thirty -five  thousandths,  .235"     "  * 

Three  hundred  and  fifty-six  ten  thousandths,  .0356"  * 

Twenty-one  thousand  and  four  hundred  thousandths,  .21004:  * 

Seven  hundred  and  forty  millionths,  .000740 

The  figures  in  a  decimal  expression  are  the  numer- 
ator of  a  decimal  fraction  ;  its  denominator  is  under- 
stood to  be  1  followed  by  as  many  ciphers  as  there 
are  decimal  places  in  the  expression ;  thus,  the  deci- 
mal fraction,  .0356,  when  written  as  a  common  frac- 
tion, is  Tf |f  o- 

The  denominator  of  a  decimal  fraction  is  always 
equal  to  1  unit,  though  it  may  be  understood  as 
tenths,  hundredths,  etc. 

Whole  numbers,  or  integers,  and  decimals,  can  be 
written  together  in  one  line  of  figures,  by  using  the 
decimal  point  to  separate  them,  because  there  is  the 
same  scale  of  increasing  or  decreasing  value  with 
both ;  thus,  2.2  is  read,  two  and  two  tenths,  and  sig- 
nifies 2  units  and  -f$  of  another  unit ;  431.56  is  read, 
four  hundred  and  thirty-one  and  fifty-six  hundredths 
of  one. 


ADD.,    SUB.,    MULT.,    D I V.    OF    DECIMALS.      173 

The  Addition,  Subtraction,  Multiplication,  and 
Division  of  Mixed  Decimals,  or  Numbers  expressing 
integers  and  decimals,  are  the  same  as  in  whole 
numbers ;  thus, 

ADDITION.          SUBTRACTION.       MULTIPLICATION.          DIVISION. 

43.2  43.20  43.2  .24)43.20(180  quotient. 

.24  _.24  .24  24 

42Maem.      1728  1920 

864  1920 


10.368  Product.  No  Bern. 

NOTE. — In  operations  in  Addition  and  Subtraction,  the  figures 
of  each  denomination  of  one  number  must  be  added  to  or  sub- 
tracted from  the  figures  of  the  same  denominations  in  the  other 
numbers ;  thereby,  the  decimal  points  will  be  under  each 
other,  and  before  the  tenths  placed  in  the  Sum  and  Remainder. 

In  Multiplication,  the  Product  must  have  as  many  decimal 
places  as  there  are  decimal  places  in  both  the  Multiplicand 
and  Multiplier.  If  necessary,  ciphers  must  be  prefixed  to  the 
product  to  make  its  number  of  decimal  places  equal. 

In  Division,  the  number  of  decimal  places  in  the  Quotient 
must  equal  the  decimal  places  in  the  Dividend  diminished  by 
the  number  of  decimal  places  in  the  Divisor.  If  necessary  to 
produce  this  result,  ciphers  must  be  prefixed  to  the  Quotient, 
or  affixed  to  the  Dividend,  and  when  both  Dividend  and  Divi- 
sor contain  the  same  number  of  decimal  places,  the  Quotient 
is  a  whole  number,  with  or  without  a  Remainder,  as  the  case 
may  be. 

Annexing  a  Cipher  on  the  right  of  a  decimal  ex- 
pression does  not  alter  its  value,  but  multiplies  both 
terms  of  the  fraction  by  10,  and  reduces  it  to  the 
next  lower  denomination;  thus,  .2 =^=.20=:-^, 
or  =  .200  =  ^. 

A  decimal,  or  a  mixed  number  of  integers  and 
decimals,  can  be  multiplied  by  10,  100,  1000,  etc.,  by 
removing  the  decimal  point  as  many  places  to  the 
right  as  there  are  ciphers  in  the  multiplier. 

Multiply  .678  by  10,  by  100,  by  1000  ;  178.9  by  10; 
19.320  by  10  ;  16.0054  x  100=  \  54.37898  x  10000  ? 
732.98x1000=? 


1  F4  EXAMPLES     IN     DECIMALS. 

Prefixing  a  Cipher  in  a  decimal  expression,  di- 
vides the  decimal  by  10,  by  removing  each  of  its  fig- 
ures one  place  farther  from  the  decimal  point ;  thus, 
.5  =  &,  .05  =  TJhr,  .005=^. 

A  decimal,  or  a  mixed  number  of  integers  and 
decimals,  can  be  divided  by  10,  100,  1000,  etc.,  by 
removing  the  decimal  point  as  many  places  to  the  left 
AS  there  are  ciphers  in  the  divisor. 

Divide  13.41  by  10,  by  100,  by  1000 ;  476.9  by  100, 
by  10000;  .17  by  10;  .176byiOOO;  43815-5-10=1 
167.009-=-10=?  -f-1000=? 

.75  of  a  metre  =  how  many  decimetres  and  centi- 
metres ?  28.03  expresses  how  many  metres,  deci- 
metres, and  centimetres  ? 

Divide  28.03  b}r  such  use  of  the  decimal  point,  so 
that  it  will  express  2  grammes  8  decigrammes  and 
3  milligrammes.  Express  3650  cents  in  dollars  and 
cents,  by  the  use  of  the  decimal  point. 

Read  45.75  in  United  States  currency,  in  French 
currency,  in  decimal  measures  of  weight,  decimal 
measures  of  capacity.  Read  196.071. 

A  Common  Fraction  can  be  changed  to  an  equiva- 
lent Decimal  Fraction,  by  dividing  its  numerator 
with  ciphers  annexed,  by  its  denominator,  and  mak- 
ing as  many  decimal  places  in  the  quotient  as  there 
are  ciphers  annexed;  thus,  J=10-r-2=5. 

Reduce  f  to  its  equivalent  decimal. 

ANALYSIS  IST. — 3  =  30  tentbs-4-8  gives  3  tenths  and  6  tenths 
remaining  ;  0  tenths  =  60  hundredths  -f-  8  gives  7  hundredths 
and  4  hundredths  remaining  ;  4  hundredths  —~  40  thousandths 
-^-8  gives  5  thousandths  and  no  remainder;  hence  f=.375. 

ANALYSIS  SND.—  |  -  fcW  =  TOT  =  ^P  =  -375. 

£  of  $1  equals  how  many  cents  ? 

.5  of  $1  equals  how  many  cents  ? 

What  is  the  decimal  expression  of  -f  ? 

.8  of  $1  equals  how  many  dimes  ? 

|  or  .75  of  $1  equals  how  much  money? 

|  of  a  metre  equals  how  many  decimetres  and 
centimetres  ? 


QUESTIOiNS,   QUERIES,   AND   PUZZLES 

FOB 

PUPILS    AT    HOME. 


1.  A  hound  is  in  pursuit  of  a  fox  that  is  10  rods  ahead  of 
him,  and  ichile  the  hound  runs  10  rods  the  fox  runs  1  rod,  (i.  e. 
while  the  hound  runs  a  certain  distance,  the  fox  runs  one-tenth 
of  that  distance.)     Will  the  hound  overtake  the  fox  ?     The 
conditions  remaining  the  same,  what  is  the  greatest  distance 
they  can  run  ? 

2.  A  hound  is  in  pursuit  of  a  fox  that  is  10  rods  ahead  of 
him,  and  while  the  fox  runa  1  rod  the  hound  runs  10  rods. 
How  far  will  the  hound  run  before  he  overtakes  the  fox  ? 

3.  Place  four  5's  in  such  a  position  that -they  shall  equal  G£, 

4.  A  boy  was  sent  to  a  spring  with  a  5  and  a  8  quart  meas- 
ure to  procure  exactly  4  quarts  of  water.    How  did  he  measure 
it? 

5.  What  is  the  difference  between  twice  25,  and  twice  5  and 
20? 

6.  A  man  had  9  pigs  and  put  them  in  4  pens,  with  an  odd 
number  of  pigs  in  each  pen.     How  did  he  divide  them  ? 

7.  Two  men  have  an  8  gallon  cask  full  of  wine,  which  they 
desire  to  divide  equally  between  them.     How  can  they  effect 
this  division,  provided'  the  only  measures  they  have  are  a  5 
gallon  cask  and  a  3  gallon  cask  ? 

8.  Place  four  2's  in  such  a  manner  that  they  shall  exactly 
equal  23. 

9.  Place  9  apples  in  10  rows  so  that  each  row  shall  contain 
3  apples. 

10.  A  squirrel  finding  9  ears  of  corn  in  a  box,  took  from  it 
daily,  3  ears;  how  many  days  was  he  in  removing  the  corn 
from  the  box  ? 

11.  If  from  six  you  take  IX,  and  from  IX  you  take  ten ;  and 
if  fifty  from  forty  be  taken,  there  will  then  just  half  a  dozen 
remain. 


1T6  QUESTIONS     AND     PUZZLES. 

12.  Edward,  Maria,  and  their  mother  went  to  market.     Ed- 
ward had  GO  apples,  and  sold  them,  at  2  for  1  cent ;  Maria  had 
60  apples,  and  sold  them,  at  3  for  1  cent.     Their  mother  had 
120  apples,  and  sold  them,  at  the  rate  of  5  for  2  cents.    Which 
received  the  most,  the  children  or  the  mother,  and  why  ? 

13.  A  gentleman  desiring  to  see  an  inmate  of  a  prison,  was 
asked  by  the  keeper  whether  he  was  related  to  the  culprit,  re- 
plied :  "  Brothers  and  sisters  have  I  none,  but  his  father  is  my 
father's  son."  What  relation  was  the  gentleman  to  the  prisoner  ? 

14.  A  man  having  a  fox,  a  goose,  and  a  peck  of  corn,  was 
desirous  of  crossing  a  river.     He  could  take  only  one  across  at 
a  time,  and  if  he  left  the  fox  and  goose,  while  he  took  the  corn 
over,  the  fox  would  kill  the  goose ;  but  if  lie  left  the  goose  and 
corn,  the  goose  would  eat  the  corn.     How  shall  he  get  them 
all  safely  across  the  river  ? 

15.  A  snail  wants  to  get  up  a  wall  20  feet  in  height,  during 
the  day  it  climbs  5  feet,  but  slips  back  4  feet  every  night ;  how 
many  days  would  it  take  to  reach  the  top  ? 

16.  A  man  purchased  a  hat  for  $5,  and  handed  the  mer- 
chant a  $50  bill  to  pay  for  it  i  the  merchant  being  unable  to 
make  the  change,  sent  the  bill  to  a  broker,  got  it  changed,  and 
then  gave  the  man  who  bought  the  hat  $45.    The  broker,  after 
the  purchaser  of  the  hat  had  gone,  discovered  that  the  bill  was 
counterfeit,  and,  therefore,  returned  it  to  the  merchant  and  re- 
ceived $50  good  money.     How  much  did  the  merchant  lose  by 
the  operation  ? 

17.  Place  ten  pennies  in  a  row,  then  carry  one  over  two, 
leaving  it  upon  the  third,  and  continue  doing  this  until  the 
ten  pennies  occupy  only  five  places,  with  two  in  each  placn. 

18.  Two  boys  laid  a  wager  as  to  which  could  lift  the  most. 
One  lifted  ninety-nine  pounds,  and  the  other  a  hundred,  and 
won.     How  m'any  pounds  did  both  lift  ? 

19.  A  frog,  at  the  bottom  of  a  well  10  feet  deep,  ascends  3 
feet  every  jump.     How  many  jumps  must  he  take  to  get  out  ? 

20.  A  drover  being  asked  how  many  horses  he  had,  replied, 
"  My  horses  together  have  twenty  fore  legs ; "  how  many  )»orse& 
had  he  ? 

21.  Write  12  in  such  a  manner,  that  you  can  show  its  half 
to  be  7. 

22.  "  I  am  constrained  to  plant  a  grove 
To  please  the  lady  that  I  lo,ve, 
This  ample  grove  is  to  compose 
Nineteen  trees  in  nine  straight  rows; 
Five  trer-s  in  each  row  I  must  place, 
Or  I  shall  never  see  her  face." 


! 


? 


Sheldon  &   Company's    Text -Books, 

Avery's   Natural   Philosophy.     460  pages.     By  ELKOY 
M.  AVERT,  A.  M. 

The  book  is  an  earnest  and  eminently  successful  attempt  to  present  the  facts 
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make  this  book  as  clear  cut  as  the  statements  and  definitions  of  the  author. 

A  Manual  of  English  Literature.  By  HENRY  MORLEY, 
Professor  of  English  Literature  in  University  College,  London. 
Thoroughly  revised,  with  an  entire  rearrangement  of  matter* 
and  with  numerous  retrenchments  and  additions,  by  MOSES 
COIT  TYLER,  Professor  of  English  Literature  in  the  University 
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For  advanced  instruction  in  English  Literature,  no  book  has  hitherto 
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Professor  Henry  Morley,  of  the  University  of  London,  is  one  of  the  most 
distinguished  living  authorities  in  all  matters  pertaining  to  English  literary 
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Professor  Moses  Coit  Tyler,  though  a  much  younger  man  than  Professor 
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country  similar  to  that  held  by  Professor  Morley  in  England.  The  combined 
labors  of  two  such  men  ought  to  give  us  the  long-needed  Text-Book  in  Eng- 
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ophy in  Chicago  University.  Royal  12ino,  cloth,  embossed. 

History  of  Ancient  and  Modern  Philosophy. 

By  Prof.  JOSEPH  HAVEN,  D.D. 

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the  life  of  the  author,  and  its  completion  and  revision  for  publication  was 
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Burritt's  Geography  of  the  Heavens.  352  pp. 

Burritt's  Celestial  Atlas.    Large  quarto. 
By  Prof.  HIKAM  MATTISON,  A.  M.,  and  ELIJAH  H.  BURRITT,  A.  M. 

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royal  octavo,  about  1400  pages. 

We  recently  published  a  copious  and  critical  Latin-English  Dictionary,  for 
the  use  of  schools,  etc.,  abridged  and  re-arranged  from  Riddle's  Latin-English 
Lexicon,  founded  on  the  German-Latin  Dictionaries  of  Dr.  Wm.  Freund  and    •, 
|  others,  by  Rev.  P.  BTTULIONS,  D.D.,  author  of  the  series  of  Grammars,  English,  i| 
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